update
This commit is contained in:
guanjihuan
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import numpy as np
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import cmath
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from math import *
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import copy
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# test
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def test():
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print('\nSuccess in the installation of GUAN package!\n')
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# basic functions
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## Pauli matrices
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def sigma_0():
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return np.eye(2)
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def sigma_x():
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return np.array([[0, 1],[1, 0]])
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def sigma_y():
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return np.array([[0, -1j],[1j, 0]])
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def sigma_z():
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return np.array([[1, 0],[0, -1]])
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## Kronecker product of Pauli matrices
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def sigma_00():
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return np.kron(sigma_0(), sigma_0())
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def sigma_0x():
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return np.kron(sigma_0(), sigma_x())
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def sigma_0y():
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return np.kron(sigma_0(), sigma_y())
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def sigma_0z():
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return np.kron(sigma_0(), sigma_z())
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def sigma_x0():
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return np.kron(sigma_x(), sigma_0())
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def sigma_xx():
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return np.kron(sigma_x(), sigma_x())
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def sigma_xy():
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return np.kron(sigma_x(), sigma_y())
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def sigma_xz():
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return np.kron(sigma_x(), sigma_z())
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def sigma_y0():
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return np.kron(sigma_y(), sigma_0())
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def sigma_yx():
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return np.kron(sigma_y(), sigma_x())
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def sigma_yy():
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return np.kron(sigma_y(), sigma_y())
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def sigma_yz():
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return np.kron(sigma_y(), sigma_z())
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def sigma_z0():
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return np.kron(sigma_z(), sigma_0())
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def sigma_zx():
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return np.kron(sigma_z(), sigma_x())
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def sigma_zy():
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return np.kron(sigma_z(), sigma_y())
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def sigma_zz():
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return np.kron(sigma_z(), sigma_z())
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# Hermitian Hamiltonian of tight binding model
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def finite_size_along_one_direction(N, on_site=0, hopping=1, period=0):
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on_site = np.array(on_site)
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hopping = np.array(hopping)
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if on_site.shape==():
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dim = 1
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else:
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dim = on_site.shape[0]
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hamiltonian = np.zeros((N*dim, N*dim), dtype=complex)
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for i0 in range(N):
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hamiltonian[i0*dim+0:i0*dim+dim, i0*dim+0:i0*dim+dim] = on_site
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for i0 in range(N-1):
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hamiltonian[i0*dim+0:i0*dim+dim, (i0+1)*dim+0:(i0+1)*dim+dim] = hopping
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hamiltonian[(i0+1)*dim+0:(i0+1)*dim+dim, i0*dim+0:i0*dim+dim] = hopping.transpose().conj()
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if period == 1:
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hamiltonian[(N-1)*dim+0:(N-1)*dim+dim, 0:dim] = hopping
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hamiltonian[0:dim, (N-1)*dim+0:(N-1)*dim+dim] = hopping.transpose().conj()
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return hamiltonian
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def finite_size_along_two_directions_for_square_lattice(N1, N2, on_site=0, hopping_1=1, hopping_2=1, period_1=0, period_2=0):
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on_site = np.array(on_site)
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hopping_1 = np.array(hopping_1)
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hopping_2 = np.array(hopping_2)
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if on_site.shape==():
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dim = 1
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else:
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dim = on_site.shape[0]
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hamiltonian = np.zeros((N1*N2*dim, N1*N2*dim), dtype=complex)
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for i1 in range(N1):
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for i2 in range(N2):
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hamiltonian[i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim, i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim] = on_site
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for i1 in range(N1-1):
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for i2 in range(N2):
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hamiltonian[i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim, (i1+1)*N2*dim+i2*dim+0:(i1+1)*N2*dim+i2*dim+dim] = hopping_1
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hamiltonian[(i1+1)*N2*dim+i2*dim+0:(i1+1)*N2*dim+i2*dim+dim, i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim] = hopping_1.transpose().conj()
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for i1 in range(N1):
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for i2 in range(N2-1):
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hamiltonian[i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim, i1*N2*dim+(i2+1)*dim+0:i1*N2*dim+(i2+1)*dim+dim] = hopping_2
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hamiltonian[i1*N2*dim+(i2+1)*dim+0:i1*N2*dim+(i2+1)*dim+dim, i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim] = hopping_2.transpose().conj()
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if period_1 == 1:
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for i2 in range(N2):
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hamiltonian[(N1-1)*N2*dim+i2*dim+0:(N1-1)*N2*dim+i2*dim+dim, i2*dim+0:i2*dim+dim] = hopping_1
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hamiltonian[i2*dim+0:i2*dim+dim, (N1-1)*N2*dim+i2*dim+0:(N1-1)*N2*dim+i2*dim+dim] = hopping_1.transpose().conj()
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if period_2 == 1:
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for i1 in range(N1):
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hamiltonian[i1*N2*dim+(N2-1)*dim+0:i1*N2*dim+(N2-1)*dim+dim, i1*N2*dim+0:i1*N2*dim+dim] = hopping_2
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hamiltonian[i1*N2*dim+0:i1*N2*dim+dim, i1*N2*dim+(N2-1)*dim+0:i1*N2*dim+(N2-1)*dim+dim] = hopping_2.transpose().conj()
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return hamiltonian
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def finite_size_along_three_directions_for_cubic_lattice(N1, N2, N3, on_site=0, hopping_1=1, hopping_2=1, hopping_3=1, period_1=0, period_2=0, period_3=0):
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on_site = np.array(on_site)
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hopping_1 = np.array(hopping_1)
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hopping_2 = np.array(hopping_2)
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hopping_3 = np.array(hopping_3)
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if on_site.shape==():
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dim = 1
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else:
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dim = on_site.shape[0]
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hamiltonian = np.zeros((N1*N2*N3*dim, N1*N2*N3*dim), dtype=complex)
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for i1 in range(N1):
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for i2 in range(N2):
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for i3 in range(N3):
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hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = on_site
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for i1 in range(N1-1):
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for i2 in range(N2):
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for i3 in range(N3):
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hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, (i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_1
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hamiltonian[(i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_1.transpose().conj()
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for i1 in range(N1):
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for i2 in range(N2-1):
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for i3 in range(N3):
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hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+dim] = hopping_2
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hamiltonian[i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_2.transpose().conj()
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for i1 in range(N1):
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for i2 in range(N2):
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for i3 in range(N3-1):
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hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+dim] = hopping_3
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hamiltonian[i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_3.transpose().conj()
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if period_1 == 1:
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for i2 in range(N2):
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for i3 in range(N3):
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hamiltonian[(N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+dim, i2*N3*dim+i3*dim+0:i2*N3*dim+i3*dim+dim] = hopping_1
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hamiltonian[i2*N3*dim+i3*dim+0:i2*N3*dim+i3*dim+dim, (N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_1.transpose().conj()
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if period_2 == 1:
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for i1 in range(N1):
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for i3 in range(N3):
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hamiltonian[i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+dim, i1*N2*N3*dim+i3*dim+0:i1*N2*N3*dim+i3*dim+dim] = hopping_2
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hamiltonian[i1*N2*N3*dim+i3*dim+0:i1*N2*N3*dim+i3*dim+dim, i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+dim] = hopping_2.transpose().conj()
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if period_3 == 1:
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for i1 in range(N1):
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for i2 in range(N2):
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hamiltonian[i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+dim, i1*N2*N3*dim+i2*N3*dim+0:i1*N2*N3*dim+i2*N3*dim+dim] = hopping_3
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hamiltonian[i1*N2*N3*dim+i2*N3*dim+0:i1*N2*N3*dim+i2*N3*dim+dim, i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+dim] = hopping_3.transpose().conj()
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return hamiltonian
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def one_dimensional_fourier_transform(k, unit_cell, hopping):
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unit_cell = np.array(unit_cell)
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hopping = np.array(hopping)
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hamiltonian = unit_cell+hopping*cmath.exp(1j*k)+hopping.transpose().conj()*cmath.exp(-1j*k)
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return hamiltonian
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def two_dimensional_fourier_transform_for_square_lattice(k1, k2, unit_cell, hopping_1, hopping_2):
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unit_cell = np.array(unit_cell)
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hopping_1 = np.array(hopping_1)
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hopping_2 = np.array(hopping_2)
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hamiltonian = unit_cell+hopping_1*cmath.exp(1j*k1)+hopping_1.transpose().conj()*cmath.exp(-1j*k1)+hopping_2*cmath.exp(1j*k2)+hopping_2.transpose().conj()*cmath.exp(-1j*k2)
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return hamiltonian
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def three_dimensional_fourier_transform_for_cubic_lattice(k1, k2, k3, unit_cell, hopping_1, hopping_2, hopping_3):
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unit_cell = np.array(unit_cell)
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hopping_1 = np.array(hopping_1)
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hopping_2 = np.array(hopping_2)
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hopping_3 = np.array(hopping_3)
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hamiltonian = unit_cell+hopping_1*cmath.exp(1j*k1)+hopping_1.transpose().conj()*cmath.exp(-1j*k1)+hopping_2*cmath.exp(1j*k2)+hopping_2.transpose().conj()*cmath.exp(-1j*k2)+hopping_3*cmath.exp(1j*k3)+hopping_3.transpose().conj()*cmath.exp(-1j*k3)
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return hamiltonian
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# Hamiltonian of graphene lattice
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def hopping_along_zigzag_direction_for_graphene(N):
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hopping = np.zeros((4*N, 4*N), dtype=complex)
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for i0 in range(N):
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hopping[4*i0+1, 4*i0+0] = 1
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hopping[4*i0+2, 4*i0+3] = 1
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return hopping
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def finite_size_along_two_directions_for_graphene(N1, N2, period_1=0, period_2=0):
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on_site = finite_size_along_one_direction(4)
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hopping_1 = hopping_along_zigzag_direction_for_graphene(1)
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hopping_2 = np.zeros((4, 4), dtype=complex)
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hopping_2[3, 0] = 1
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hamiltonian = finite_size_along_two_directions_for_square_lattice(N1, N2, on_site, hopping_1, hopping_2, period_1, period_2)
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return hamiltonian
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# calculate band structures
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def calculate_eigenvalue(hamiltonian):
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if np.array(hamiltonian).shape==():
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eigenvalue = np.real(hamiltonian)
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else:
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eigenvalue, eigenvector = np.linalg.eig(hamiltonian)
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eigenvalue = np.sort(np.real(eigenvalue))
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return eigenvalue
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def calculate_eigenvalue_with_one_parameter(x, hamiltonian_function):
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dim_x = np.array(x).shape[0]
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i0 = 0
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if np.array(hamiltonian_function(0)).shape==():
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eigenvalue_array = np.zeros((dim_x, 1))
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for x0 in x:
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hamiltonian = hamiltonian_function(x0)
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eigenvalue_array[i0, 0] = np.real(hamiltonian)
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i0 += 1
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else:
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dim = np.array(hamiltonian_function(0)).shape[0]
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eigenvalue_array = np.zeros((dim_x, dim))
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for x0 in x:
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hamiltonian = hamiltonian_function(x0)
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eigenvalue, eigenvector = np.linalg.eig(hamiltonian)
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eigenvalue_array[i0, :] = np.sort(np.real(eigenvalue[:]))
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i0 += 1
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return eigenvalue_array
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def calculate_eigenvalue_with_two_parameters(x, y, hamiltonian_function):
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dim_x = np.array(x).shape[0]
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dim_y = np.array(y).shape[0]
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if np.array(hamiltonian_function(0,0)).shape==():
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eigenvalue_array = np.zeros((dim_y, dim_x, 1))
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i0 = 0
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for y0 in y:
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j0 = 0
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for x0 in x:
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hamiltonian = hamiltonian_function(x0, y0)
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eigenvalue_array[i0, j0, 0] = np.real(hamiltonian)
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j0 += 1
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i0 += 1
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else:
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||||||
dim = np.array(hamiltonian_function(0, 0)).shape[0]
|
|
||||||
eigenvalue_array = np.zeros((dim_y, dim_x, dim))
|
|
||||||
i0 = 0
|
|
||||||
for y0 in y:
|
|
||||||
j0 = 0
|
|
||||||
for x0 in x:
|
|
||||||
hamiltonian = hamiltonian_function(x0, y0)
|
|
||||||
eigenvalue, eigenvector = np.linalg.eig(hamiltonian)
|
|
||||||
eigenvalue_array[i0, j0, :] = np.sort(np.real(eigenvalue[:]))
|
|
||||||
j0 += 1
|
|
||||||
i0 += 1
|
|
||||||
return eigenvalue_array
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# calculate wave functions
|
|
||||||
|
|
||||||
def calculate_eigenvector(hamiltonian):
|
|
||||||
eigenvalue, eigenvector = np.linalg.eig(hamiltonian)
|
|
||||||
eigenvector = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
|
||||||
return eigenvector
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# calculate Green functions
|
|
||||||
|
|
||||||
def green_function(fermi_energy, hamiltonian, broadening, self_energy=0):
|
|
||||||
if np.array(hamiltonian).shape==():
|
|
||||||
dim = 1
|
|
||||||
else:
|
|
||||||
dim = np.array(hamiltonian).shape[0]
|
|
||||||
green = np.linalg.inv((fermi_energy+broadening*1j)*np.eye(dim)-hamiltonian-self_energy)
|
|
||||||
return green
|
|
||||||
|
|
||||||
|
|
||||||
def green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening, self_energy=0):
|
|
||||||
h01 = np.array(h01)
|
|
||||||
if np.array(h00).shape==():
|
|
||||||
dim = 1
|
|
||||||
else:
|
|
||||||
dim = np.array(h00).shape[0]
|
|
||||||
green_nn_n = np.linalg.inv((fermi_energy+broadening*1j)*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), green_nn_n_minus), h01)-self_energy)
|
|
||||||
return green_nn_n
|
|
||||||
|
|
||||||
|
|
||||||
def green_function_in_n(green_in_n_minus, h01, green_nn_n):
|
|
||||||
green_in_n = np.dot(np.dot(green_in_n_minus, h01), green_nn_n)
|
|
||||||
return green_in_n
|
|
||||||
|
|
||||||
|
|
||||||
def green_function_ni_n(green_nn_n, h01, green_ni_n_minus):
|
|
||||||
h01 = np.array(h01)
|
|
||||||
green_ni_n = np.dot(np.dot(green_nn_n, h01.transpose().conj()), green_ni_n_minus)
|
|
||||||
return green_ni_n
|
|
||||||
|
|
||||||
|
|
||||||
def green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus):
|
|
||||||
green_ii_n = green_ii_n_minus+np.dot(np.dot(np.dot(np.dot(green_in_n_minus, h01), green_nn_n), h01.transpose().conj()),green_ni_n_minus)
|
|
||||||
return green_ii_n
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# calculate density of states
|
|
||||||
|
|
||||||
def total_density_of_states(fermi_energy, hamiltonian, broadening=0.01):
|
|
||||||
green = green_function(fermi_energy, hamiltonian, broadening)
|
|
||||||
total_dos = -np.trace(np.imag(green))/pi
|
|
||||||
return total_dos
|
|
||||||
|
|
||||||
|
|
||||||
def total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.01):
|
|
||||||
dim = np.array(fermi_energy_array).shape[0]
|
|
||||||
total_dos_array = np.zeros(dim)
|
|
||||||
i0 = 0
|
|
||||||
for fermi_energy in fermi_energy_array:
|
|
||||||
total_dos_array[i0] = total_density_of_states(fermi_energy, hamiltonian, broadening)
|
|
||||||
i0 += 1
|
|
||||||
return total_dos_array
|
|
||||||
|
|
||||||
|
|
||||||
def local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1, N2, internal_degree=1, broadening=0.01):
|
|
||||||
# dim_hamiltonian = N1*N2*internal_degree
|
|
||||||
green = green_function(fermi_energy, hamiltonian, broadening)
|
|
||||||
local_dos = np.zeros((N2, N1))
|
|
||||||
for i1 in range(N1):
|
|
||||||
for i2 in range(N2):
|
|
||||||
for i in range(internal_degree):
|
|
||||||
local_dos[i2, i1] = local_dos[i2, i1]-np.imag(green[i1*N2*internal_degree+i2*internal_degree+i, i1*N2*internal_degree+i2*internal_degree+i])/pi
|
|
||||||
return local_dos
|
|
||||||
|
|
||||||
|
|
||||||
def local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1, N2, N3, internal_degree=1, broadening=0.01):
|
|
||||||
# dim_hamiltonian = N1*N2*N3*internal_degree
|
|
||||||
green = green_function(fermi_energy, hamiltonian, broadening)
|
|
||||||
local_dos = np.zeros((N3, N2, N1))
|
|
||||||
for i1 in range(N1):
|
|
||||||
for i2 in range(N2):
|
|
||||||
for i3 in range(N3):
|
|
||||||
for i in range(internal_degree):
|
|
||||||
local_dos[i3, i2, i1] = local_dos[i3, i2, i1]-np.imag(green[i1*N2*N3*internal_degree+i2*N3*internal_degree+i3*internal_degree+i, i1*N2*N3*internal_degree+i2*N3*internal_degree+i3*internal_degree+i])/pi
|
|
||||||
return local_dos
|
|
||||||
|
|
||||||
|
|
||||||
def local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00, h01, N2, N1, internal_degree=1, broadening=0.01):
|
|
||||||
# dim_h00 = N2*internal_degree
|
|
||||||
local_dos = np.zeros((N2, N1))
|
|
||||||
green_11_1 = green_function(fermi_energy, h00, broadening)
|
|
||||||
for i1 in range(N1):
|
|
||||||
green_nn_n_minus = green_11_1
|
|
||||||
green_in_n_minus = green_11_1
|
|
||||||
green_ni_n_minus = green_11_1
|
|
||||||
green_ii_n_minus = green_11_1
|
|
||||||
for i2_0 in range(i1):
|
|
||||||
green_nn_n = green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
|
||||||
green_nn_n_minus = green_nn_n
|
|
||||||
if i1!=0:
|
|
||||||
green_in_n_minus = green_nn_n
|
|
||||||
green_ni_n_minus = green_nn_n
|
|
||||||
green_ii_n_minus = green_nn_n
|
|
||||||
for size_0 in range(N1-1-i1):
|
|
||||||
green_nn_n = green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
|
||||||
green_nn_n_minus = green_nn_n
|
|
||||||
green_ii_n = green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus)
|
|
||||||
green_ii_n_minus = green_ii_n
|
|
||||||
green_in_n = green_function_in_n(green_in_n_minus, h01, green_nn_n)
|
|
||||||
green_in_n_minus = green_in_n
|
|
||||||
green_ni_n = green_function_ni_n(green_nn_n, h01, green_ni_n_minus)
|
|
||||||
green_ni_n_minus = green_ni_n
|
|
||||||
for i2 in range(N2):
|
|
||||||
for i in range(internal_degree):
|
|
||||||
local_dos[i2, i1] = local_dos[i2, i1] - np.imag(green_ii_n_minus[i2*internal_degree+i, i2*internal_degree+i])/pi
|
|
||||||
return local_dos
|
|
||||||
|
|
||||||
|
|
||||||
def local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3, N2, N1, internal_degree=1, broadening=0.01):
|
|
||||||
# dim_h00 = N2*N3*internal_degree
|
|
||||||
local_dos = np.zeros((N3, N2, N1))
|
|
||||||
green_11_1 = green_function(fermi_energy, h00, broadening)
|
|
||||||
for i1 in range(N1):
|
|
||||||
green_nn_n_minus = green_11_1
|
|
||||||
green_in_n_minus = green_11_1
|
|
||||||
green_ni_n_minus = green_11_1
|
|
||||||
green_ii_n_minus = green_11_1
|
|
||||||
for i1_0 in range(i1):
|
|
||||||
green_nn_n = green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
|
||||||
green_nn_n_minus = green_nn_n
|
|
||||||
if i1!=0:
|
|
||||||
green_in_n_minus = green_nn_n
|
|
||||||
green_ni_n_minus = green_nn_n
|
|
||||||
green_ii_n_minus = green_nn_n
|
|
||||||
for size_0 in range(N1-1-i1):
|
|
||||||
green_nn_n = green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
|
||||||
green_nn_n_minus = green_nn_n
|
|
||||||
green_ii_n = green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus)
|
|
||||||
green_ii_n_minus = green_ii_n
|
|
||||||
green_in_n = green_function_in_n(green_in_n_minus, h01, green_nn_n)
|
|
||||||
green_in_n_minus = green_in_n
|
|
||||||
green_ni_n = green_function_ni_n(green_nn_n, h01, green_ni_n_minus)
|
|
||||||
green_ni_n_minus = green_ni_n
|
|
||||||
for i2 in range(N2):
|
|
||||||
for i3 in range(N3):
|
|
||||||
for i in range(internal_degree):
|
|
||||||
local_dos[i3, i2, i1] = local_dos[i3, i2, i1] -np.imag(green_ii_n_minus[i2*N3*internal_degree+i3*internal_degree+i, i2*N3*internal_degree+i3*internal_degree+i])/pi
|
|
||||||
return local_dos
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# calculate conductance
|
|
||||||
|
|
||||||
def transfer_matrix(fermi_energy, h00, h01):
|
|
||||||
h01 = np.array(h01)
|
|
||||||
if np.array(h00).shape==():
|
|
||||||
dim = 1
|
|
||||||
else:
|
|
||||||
dim = np.array(h00).shape[0]
|
|
||||||
transfer = np.zeros((2*dim, 2*dim), dtype=complex)
|
|
||||||
transfer[0:dim, 0:dim] = np.dot(np.linalg.inv(h01), fermi_energy*np.identity(dim)-h00)
|
|
||||||
transfer[0:dim, dim:2*dim] = np.dot(-1*np.linalg.inv(h01), h01.transpose().conj())
|
|
||||||
transfer[dim:2*dim, 0:dim] = np.identity(dim)
|
|
||||||
transfer[dim:2*dim, dim:2*dim] = 0
|
|
||||||
return transfer
|
|
||||||
|
|
||||||
|
|
||||||
def surface_green_function_of_lead(fermi_energy, h00, h01):
|
|
||||||
h01 = np.array(h01)
|
|
||||||
if np.array(h00).shape==():
|
|
||||||
dim = 1
|
|
||||||
else:
|
|
||||||
dim = np.array(h00).shape[0]
|
|
||||||
fermi_energy = fermi_energy+1e-9*1j
|
|
||||||
transfer = transfer_matrix(fermi_energy, h00, h01)
|
|
||||||
eigenvalue, eigenvector = np.linalg.eig(transfer)
|
|
||||||
ind = np.argsort(np.abs(eigenvalue))
|
|
||||||
temp = np.zeros((2*dim, 2*dim), dtype=complex)
|
|
||||||
i0 = 0
|
|
||||||
for ind0 in ind:
|
|
||||||
temp[:, i0] = eigenvector[:, ind0]
|
|
||||||
i0 += 1
|
|
||||||
s1 = temp[dim:2*dim, 0:dim]
|
|
||||||
s2 = temp[0:dim, 0:dim]
|
|
||||||
s3 = temp[dim:2*dim, dim:2*dim]
|
|
||||||
s4 = temp[0:dim, dim:2*dim]
|
|
||||||
right_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01, s2), np.linalg.inv(s1)))
|
|
||||||
left_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), s3), np.linalg.inv(s4)))
|
|
||||||
return right_lead_surface, left_lead_surface
|
|
||||||
|
|
||||||
|
|
||||||
def self_energy_of_lead(fermi_energy, h00, h01):
|
|
||||||
h01 = np.array(h01)
|
|
||||||
right_lead_surface, left_lead_surface = surface_green_function_of_lead(fermi_energy, h00, h01)
|
|
||||||
right_self_energy = np.dot(np.dot(h01, right_lead_surface), h01.transpose().conj())
|
|
||||||
left_self_energy = np.dot(np.dot(h01.transpose().conj(), left_lead_surface), h01)
|
|
||||||
return right_self_energy, left_self_energy
|
|
||||||
|
|
||||||
|
|
||||||
def calculate_conductance(fermi_energy, h00, h01, length=100):
|
|
||||||
right_self_energy, left_self_energy = self_energy_of_lead(fermi_energy, h00, h01)
|
|
||||||
for ix in range(length):
|
|
||||||
if ix == 0:
|
|
||||||
green_nn_n = green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
|
||||||
green_0n_n = copy.deepcopy(green_nn_n)
|
|
||||||
elif ix != length-1:
|
|
||||||
green_nn_n = green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
|
|
||||||
green_0n_n = green_function_in_n(green_0n_n, h01, green_nn_n)
|
|
||||||
else:
|
|
||||||
green_nn_n = green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
|
||||||
green_0n_n = green_function_in_n(green_0n_n, h01, green_nn_n)
|
|
||||||
right_self_energy = (right_self_energy - right_self_energy.transpose().conj())*(0+1j)
|
|
||||||
left_self_energy = (left_self_energy - left_self_energy.transpose().conj())*(0+1j)
|
|
||||||
conductance = np.trace(np.dot(np.dot(np.dot(left_self_energy, green_0n_n), right_self_energy), green_0n_n.transpose().conj()))
|
|
||||||
return conductance
|
|
||||||
|
|
||||||
|
|
||||||
def calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01, length=100):
|
|
||||||
dim = np.array(fermi_energy_array).shape[0]
|
|
||||||
conductance_array = np.zeros(dim)
|
|
||||||
i0 = 0
|
|
||||||
for fermi_energy_0 in fermi_energy_array:
|
|
||||||
conductance_array[i0] = np.real(calculate_conductance(fermi_energy_0, h00, h01, length))
|
|
||||||
i0 += 1
|
|
||||||
return conductance_array
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# calculate scattering matrix
|
|
||||||
|
|
||||||
def if_active_channel(k_of_channel):
|
|
||||||
if np.abs(np.imag(k_of_channel))<1e-6:
|
|
||||||
if_active = 1
|
|
||||||
else:
|
|
||||||
if_active = 0
|
|
||||||
return if_active
|
|
||||||
|
|
||||||
|
|
||||||
def get_k_and_velocity_of_channel(fermi_energy, h00, h01):
|
|
||||||
if np.array(h00).shape==():
|
|
||||||
dim = 1
|
|
||||||
else:
|
|
||||||
dim = np.array(h00).shape[0]
|
|
||||||
transfer = transfer_matrix(fermi_energy, h00, h01)
|
|
||||||
eigenvalue, eigenvector = np.linalg.eig(transfer)
|
|
||||||
k_of_channel = np.log(eigenvalue)/1j
|
|
||||||
ind = np.argsort(np.real(k_of_channel))
|
|
||||||
k_of_channel = np.sort(k_of_channel)
|
|
||||||
temp = np.zeros((2*dim, 2*dim), dtype=complex)
|
|
||||||
temp2 = np.zeros((2*dim), dtype=complex)
|
|
||||||
i0 = 0
|
|
||||||
for ind0 in ind:
|
|
||||||
temp[:, i0] = eigenvector[:, ind0]
|
|
||||||
temp2[i0] = eigenvalue[ind0]
|
|
||||||
i0 += 1
|
|
||||||
eigenvalue = copy.deepcopy(temp2)
|
|
||||||
temp = temp[0:dim, :]
|
|
||||||
factor = np.zeros(2*dim, dtype=complex)
|
|
||||||
for dim0 in range(dim):
|
|
||||||
factor = factor+np.square(np.abs(temp[dim0, :]))
|
|
||||||
for dim0 in range(2*dim):
|
|
||||||
temp[:, dim0] = temp[:, dim0]/np.sqrt(factor[dim0])
|
|
||||||
velocity_of_channel = np.zeros((2*dim), dtype=complex)
|
|
||||||
for dim0 in range(2*dim):
|
|
||||||
velocity_of_channel[dim0] = eigenvalue[dim0]*np.dot(np.dot(temp[0:dim, :].transpose().conj(), h01),temp[0:dim, :])[dim0, dim0]
|
|
||||||
velocity_of_channel = -2*np.imag(velocity_of_channel)
|
|
||||||
eigenvector = copy.deepcopy(temp)
|
|
||||||
return k_of_channel, velocity_of_channel, eigenvalue, eigenvector
|
|
||||||
|
|
||||||
|
|
||||||
def get_classified_k_velocity_u_and_f(fermi_energy, h00, h01):
|
|
||||||
if np.array(h00).shape==():
|
|
||||||
dim = 1
|
|
||||||
else:
|
|
||||||
dim = np.array(h00).shape[0]
|
|
||||||
k_of_channel, velocity_of_channel, eigenvalue, eigenvector = get_k_and_velocity_of_channel(fermi_energy, h00, h01)
|
|
||||||
ind_right_active = 0; ind_right_evanescent = 0; ind_left_active = 0; ind_left_evanescent = 0
|
|
||||||
k_right = np.zeros(dim, dtype=complex); k_left = np.zeros(dim, dtype=complex)
|
|
||||||
velocity_right = np.zeros(dim, dtype=complex); velocity_left = np.zeros(dim, dtype=complex)
|
|
||||||
lambda_right = np.zeros(dim, dtype=complex); lambda_left = np.zeros(dim, dtype=complex)
|
|
||||||
u_right = np.zeros((dim, dim), dtype=complex); u_left = np.zeros((dim, dim), dtype=complex)
|
|
||||||
for dim0 in range(2*dim):
|
|
||||||
if_active = if_active_channel(k_of_channel[dim0])
|
|
||||||
if if_active_channel(k_of_channel[dim0]) == 1:
|
|
||||||
direction = np.sign(velocity_of_channel[dim0])
|
|
||||||
else:
|
|
||||||
direction = np.sign(np.imag(k_of_channel[dim0]))
|
|
||||||
if direction == 1:
|
|
||||||
if if_active == 1: # right-moving active channel
|
|
||||||
k_right[ind_right_active] = k_of_channel[dim0]
|
|
||||||
velocity_right[ind_right_active] = velocity_of_channel[dim0]
|
|
||||||
lambda_right[ind_right_active] = eigenvalue[dim0]
|
|
||||||
u_right[:, ind_right_active] = eigenvector[:, dim0]
|
|
||||||
ind_right_active += 1
|
|
||||||
else: # right-moving evanescent channel
|
|
||||||
k_right[dim-1-ind_right_evanescent] = k_of_channel[dim0]
|
|
||||||
velocity_right[dim-1-ind_right_evanescent] = velocity_of_channel[dim0]
|
|
||||||
lambda_right[dim-1-ind_right_evanescent] = eigenvalue[dim0]
|
|
||||||
u_right[:, dim-1-ind_right_evanescent] = eigenvector[:, dim0]
|
|
||||||
ind_right_evanescent += 1
|
|
||||||
else:
|
|
||||||
if if_active == 1: # left-moving active channel
|
|
||||||
k_left[ind_left_active] = k_of_channel[dim0]
|
|
||||||
velocity_left[ind_left_active] = velocity_of_channel[dim0]
|
|
||||||
lambda_left[ind_left_active] = eigenvalue[dim0]
|
|
||||||
u_left[:, ind_left_active] = eigenvector[:, dim0]
|
|
||||||
ind_left_active += 1
|
|
||||||
else: # left-moving evanescent channel
|
|
||||||
k_left[dim-1-ind_left_evanescent] = k_of_channel[dim0]
|
|
||||||
velocity_left[dim-1-ind_left_evanescent] = velocity_of_channel[dim0]
|
|
||||||
lambda_left[dim-1-ind_left_evanescent] = eigenvalue[dim0]
|
|
||||||
u_left[:, dim-1-ind_left_evanescent] = eigenvector[:, dim0]
|
|
||||||
ind_left_evanescent += 1
|
|
||||||
lambda_matrix_right = np.diag(lambda_right)
|
|
||||||
lambda_matrix_left = np.diag(lambda_left)
|
|
||||||
f_right = np.dot(np.dot(u_right, lambda_matrix_right), np.linalg.inv(u_right))
|
|
||||||
f_left = np.dot(np.dot(u_left, lambda_matrix_left), np.linalg.inv(u_left))
|
|
||||||
return k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active
|
|
||||||
|
|
||||||
|
|
||||||
def calculate_scattering_matrix(fermi_energy, h00, h01, length=100):
|
|
||||||
h01 = np.array(h01)
|
|
||||||
if np.array(h00).shape==():
|
|
||||||
dim = 1
|
|
||||||
else:
|
|
||||||
dim = np.array(h00).shape[0]
|
|
||||||
k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active = get_classified_k_velocity_u_and_f(fermi_energy, h00, h01)
|
|
||||||
right_self_energy = np.dot(h01, f_right)
|
|
||||||
left_self_energy = np.dot(h01.transpose().conj(), np.linalg.inv(f_left))
|
|
||||||
for i0 in range(length):
|
|
||||||
if i0 == 0:
|
|
||||||
green_nn_n = green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
|
||||||
green_00_n = copy.deepcopy(green_nn_n)
|
|
||||||
green_0n_n = copy.deepcopy(green_nn_n)
|
|
||||||
green_n0_n = copy.deepcopy(green_nn_n)
|
|
||||||
elif i0 != length-1:
|
|
||||||
green_nn_n = green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
|
|
||||||
else:
|
|
||||||
green_nn_n = green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
|
||||||
green_00_n = green_function_ii_n(green_00_n, green_0n_n, h01, green_nn_n, green_n0_n)
|
|
||||||
green_0n_n = green_function_in_n(green_0n_n, h01, green_nn_n)
|
|
||||||
green_n0_n = green_function_ni_n(green_nn_n, h01, green_n0_n)
|
|
||||||
temp = np.dot(h01.transpose().conj(), np.linalg.inv(f_right)-np.linalg.inv(f_left))
|
|
||||||
transmission_matrix = np.dot(np.dot(np.linalg.inv(u_right), np.dot(green_n0_n, temp)), u_right)
|
|
||||||
reflection_matrix = np.dot(np.dot(np.linalg.inv(u_left), np.dot(green_00_n, temp)-np.identity(dim)), u_right)
|
|
||||||
for dim0 in range(dim):
|
|
||||||
for dim1 in range(dim):
|
|
||||||
if_active = if_active_channel(k_right[dim0])*if_active_channel(k_right[dim1])
|
|
||||||
if if_active == 1:
|
|
||||||
transmission_matrix[dim0, dim1] = np.sqrt(np.abs(velocity_right[dim0]/velocity_right[dim1])) * transmission_matrix[dim0, dim1]
|
|
||||||
reflection_matrix[dim0, dim1] = np.sqrt(np.abs(velocity_left[dim0]/velocity_right[dim1]))*reflection_matrix[dim0, dim1]
|
|
||||||
else:
|
|
||||||
transmission_matrix[dim0, dim1] = 0
|
|
||||||
reflection_matrix[dim0, dim1] = 0
|
|
||||||
sum_of_tran_refl_array = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)+np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
|
||||||
for sum_of_tran_refl in sum_of_tran_refl_array:
|
|
||||||
if sum_of_tran_refl > 1.001:
|
|
||||||
print('Error Alert: scattering matrix is not normalized!')
|
|
||||||
return transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active
|
|
||||||
|
|
||||||
|
|
||||||
def print_or_write_scattering_matrix(fermi_energy, h00, h01, length=100, on_print=1, on_write=0):
|
|
||||||
if np.array(h00).shape==():
|
|
||||||
dim = 1
|
|
||||||
else:
|
|
||||||
dim = np.array(h00).shape[0]
|
|
||||||
transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = calculate_scattering_matrix(fermi_energy, h00, h01, length)
|
|
||||||
if on_print == 1:
|
|
||||||
print('\nActive channel (left or right) = ', ind_right_active)
|
|
||||||
print('Evanescent channel (left or right) = ', dim-ind_right_active, '\n')
|
|
||||||
print('K of right-moving active channels:\n', np.real(k_right[0:ind_right_active]))
|
|
||||||
print('K of left-moving active channels:\n', np.real(k_left[0:ind_right_active]), '\n')
|
|
||||||
print('Velocity of right-moving active channels:\n', np.real(velocity_right[0:ind_right_active]))
|
|
||||||
print('Velocity of left-moving active channels:\n', np.real(velocity_left[0:ind_right_active]), '\n')
|
|
||||||
print('Transmission matrix:\n', np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])))
|
|
||||||
print('Reflection matrix:\n', np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), '\n')
|
|
||||||
print('Total transmission of channels:\n', np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0))
|
|
||||||
print('Total reflection of channels:\n',np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0))
|
|
||||||
print('Sum of transmission and reflection of channels:\n', np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0) + np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0))
|
|
||||||
print('Total conductance = ', np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active]))), '\n')
|
|
||||||
if on_write == 1:
|
|
||||||
with open('a.txt', 'w') as f:
|
|
||||||
f.write('Active channel (left or right) = ' + str(ind_right_active) + '\n')
|
|
||||||
f.write('Evanescent channel (left or right) = ' + str(dim - ind_right_active) + '\n\n')
|
|
||||||
f.write('Channel K Velocity\n')
|
|
||||||
for ind0 in range(ind_right_active):
|
|
||||||
f.write(' '+str(ind0 + 1) + ' | '+str(np.real(k_right[ind0]))+' ' + str(np.real(velocity_right[ind0]))+'\n')
|
|
||||||
f.write('\n')
|
|
||||||
for ind0 in range(ind_right_active):
|
|
||||||
f.write(' -' + str(ind0 + 1) + ' | ' + str(np.real(k_left[ind0])) + ' ' + str(np.real(velocity_left[ind0])) + '\n')
|
|
||||||
f.write('\nScattering matrix:\n ')
|
|
||||||
for ind0 in range(ind_right_active):
|
|
||||||
f.write(str(ind0+1)+' ')
|
|
||||||
f.write('\n')
|
|
||||||
for ind1 in range(ind_right_active):
|
|
||||||
f.write(' '+str(ind1+1)+' ')
|
|
||||||
for ind2 in range(ind_right_active):
|
|
||||||
f.write('%f' % np.square(np.abs(transmission_matrix[ind1, ind2]))+' ')
|
|
||||||
f.write('\n')
|
|
||||||
f.write('\n')
|
|
||||||
for ind1 in range(ind_right_active):
|
|
||||||
f.write(' -'+str(ind1+1)+' ')
|
|
||||||
for ind2 in range(ind_right_active):
|
|
||||||
f.write('%f' % np.square(np.abs(reflection_matrix[ind1, ind2]))+' ')
|
|
||||||
f.write('\n')
|
|
||||||
f.write('\n')
|
|
||||||
f.write('Total transmission of channels:\n'+str(np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0))+'\n')
|
|
||||||
f.write('Total conductance = '+str(np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active]))))+'\n')
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# calculate Chern number
|
|
||||||
|
|
||||||
def calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100):
|
|
||||||
if np.array(hamiltonian_function(0, 0)).shape==():
|
|
||||||
dim = 1
|
|
||||||
else:
|
|
||||||
dim = np.array(hamiltonian_function(0, 0)).shape[0]
|
|
||||||
delta = 2*pi/precision
|
|
||||||
chern_number = np.zeros(dim, dtype=complex)
|
|
||||||
for kx in np.arange(-pi, pi, delta):
|
|
||||||
for ky in np.arange(-pi, pi, delta):
|
|
||||||
H = hamiltonian_function(kx, ky)
|
|
||||||
vector = calculate_eigenvector(H)
|
|
||||||
H_delta_kx = hamiltonian_function(kx+delta, ky)
|
|
||||||
vector_delta_kx = calculate_eigenvector(H_delta_kx)
|
|
||||||
H_delta_ky = hamiltonian_function(kx, ky+delta)
|
|
||||||
vector_delta_ky = calculate_eigenvector(H_delta_ky)
|
|
||||||
H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
|
|
||||||
vector_delta_kx_ky = calculate_eigenvector(H_delta_kx_ky)
|
|
||||||
for i in range(dim):
|
|
||||||
vector_i = vector[:, i]
|
|
||||||
vector_delta_kx_i = vector_delta_kx[:, i]
|
|
||||||
vector_delta_ky_i = vector_delta_ky[:, i]
|
|
||||||
vector_delta_kx_ky_i = vector_delta_kx_ky[:, i]
|
|
||||||
Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i))
|
|
||||||
Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i))
|
|
||||||
Ux_y = np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i))
|
|
||||||
Uy_x = np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i))
|
|
||||||
F = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))
|
|
||||||
chern_number[i] = chern_number[i] + F
|
|
||||||
chern_number = chern_number/(2*pi*1j)
|
|
||||||
return chern_number
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# calculate Wilson loop
|
|
||||||
|
|
||||||
def calculate_wilson_loop(hamiltonian_function, k_min=-pi, k_max=pi, precision=100):
|
|
||||||
k_array = np.linspace(k_min, k_max, precision)
|
|
||||||
dim = np.array(hamiltonian_function(0)).shape[0]
|
|
||||||
wilson_loop_array = np.ones(dim, dtype=complex)
|
|
||||||
for i in range(dim):
|
|
||||||
eigenvector_array = []
|
|
||||||
for k in k_array:
|
|
||||||
eigenvector = calculate_eigenvector(hamiltonian_function(k))
|
|
||||||
if k != k_max:
|
|
||||||
eigenvector_array.append(eigenvector[:, i])
|
|
||||||
else:
|
|
||||||
eigenvector_array.append(eigenvector_array[0])
|
|
||||||
for i0 in range(precision-1):
|
|
||||||
F = np.dot(eigenvector_array[i0+1].transpose().conj(), eigenvector_array[i0])
|
|
||||||
wilson_loop_array[i] = np.dot(F, wilson_loop_array[i])
|
|
||||||
return wilson_loop_array
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# read and write
|
|
||||||
|
|
||||||
def read_one_dimensional_data(filename='a'):
|
|
||||||
f = open(filename+'.txt', 'r')
|
|
||||||
text = f.read()
|
|
||||||
f.close()
|
|
||||||
row_list = np.array(text.split('\n'))
|
|
||||||
dim_column = np.array(row_list[0].split()).shape[0]
|
|
||||||
x = np.array([])
|
|
||||||
y = np.array([])
|
|
||||||
for row in row_list:
|
|
||||||
column = np.array(row.split())
|
|
||||||
if column.shape[0] != 0:
|
|
||||||
x = np.append(x, [float(column[0])], axis=0)
|
|
||||||
y_row = np.zeros(dim_column-1)
|
|
||||||
for dim0 in range(dim_column-1):
|
|
||||||
y_row[dim0] = float(column[dim0+1])
|
|
||||||
if np.array(y).shape[0] == 0:
|
|
||||||
y = [y_row]
|
|
||||||
else:
|
|
||||||
y = np.append(y, [y_row], axis=0)
|
|
||||||
return x, y
|
|
||||||
|
|
||||||
|
|
||||||
def read_two_dimensional_data(filename='a'):
|
|
||||||
f = open(filename+'.txt', 'r')
|
|
||||||
text = f.read()
|
|
||||||
f.close()
|
|
||||||
row_list = np.array(text.split('\n'))
|
|
||||||
dim_column = np.array(row_list[0].split()).shape[0]
|
|
||||||
x = np.array([])
|
|
||||||
y = np.array([])
|
|
||||||
matrix = np.array([])
|
|
||||||
for i0 in range(row_list.shape[0]):
|
|
||||||
column = np.array(row_list[i0].split())
|
|
||||||
if i0 == 0:
|
|
||||||
x_str = column[1::]
|
|
||||||
x = np.zeros(x_str.shape[0])
|
|
||||||
for i00 in range(x_str.shape[0]):
|
|
||||||
x[i00] = float(x_str[i00])
|
|
||||||
elif column.shape[0] != 0:
|
|
||||||
y = np.append(y, [float(column[0])], axis=0)
|
|
||||||
matrix_row = np.zeros(dim_column-1)
|
|
||||||
for dim0 in range(dim_column-1):
|
|
||||||
matrix_row[dim0] = float(column[dim0+1])
|
|
||||||
if np.array(matrix).shape[0] == 0:
|
|
||||||
matrix = [matrix_row]
|
|
||||||
else:
|
|
||||||
matrix = np.append(matrix, [matrix_row], axis=0)
|
|
||||||
return x, y, matrix
|
|
||||||
|
|
||||||
|
|
||||||
def write_one_dimensional_data(x, y, filename='a'):
|
|
||||||
with open(filename+'.txt', 'w') as f:
|
|
||||||
i0 = 0
|
|
||||||
for x0 in x:
|
|
||||||
f.write(str(x0)+' ')
|
|
||||||
if len(y.shape) == 1:
|
|
||||||
f.write(str(y[i0])+'\n')
|
|
||||||
elif len(y.shape) == 2:
|
|
||||||
for j0 in range(y.shape[1]):
|
|
||||||
f.write(str(y[i0, j0])+' ')
|
|
||||||
f.write('\n')
|
|
||||||
i0 += 1
|
|
||||||
|
|
||||||
|
|
||||||
def write_two_dimensional_data(x, y, matrix, filename='a'):
|
|
||||||
with open(filename+'.txt', 'w') as f:
|
|
||||||
f.write('0 ')
|
|
||||||
for x0 in x:
|
|
||||||
f.write(str(x0)+' ')
|
|
||||||
f.write('\n')
|
|
||||||
i0 = 0
|
|
||||||
for y0 in y:
|
|
||||||
f.write(str(y0))
|
|
||||||
j0 = 0
|
|
||||||
for x0 in x:
|
|
||||||
f.write(' '+str(matrix[i0, j0])+' ')
|
|
||||||
j0 += 1
|
|
||||||
f.write('\n')
|
|
||||||
i0 += 1
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# plot figures
|
|
||||||
|
|
||||||
def plot(x, y, xlabel='x', ylabel='y', title='', filename='a', show=1, save=0, type='', y_min=None, y_max=None):
|
|
||||||
import matplotlib.pyplot as plt
|
|
||||||
fig, ax = plt.subplots()
|
|
||||||
plt.subplots_adjust(bottom=0.20, left=0.18)
|
|
||||||
ax.plot(x, y, type)
|
|
||||||
ax.grid()
|
|
||||||
ax.set_title(title, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
ax.set_xlabel(xlabel, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
ax.set_ylabel(ylabel, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
if y_min!=None or y_max!=None:
|
|
||||||
if y_min==None:
|
|
||||||
y_min=min(y)
|
|
||||||
if y_max==None:
|
|
||||||
y_max=max(y)
|
|
||||||
ax.set_ylim(y_min, y_max)
|
|
||||||
ax.tick_params(labelsize=20)
|
|
||||||
labels = ax.get_xticklabels() + ax.get_yticklabels()
|
|
||||||
[label.set_fontname('Times New Roman') for label in labels]
|
|
||||||
if save == 1:
|
|
||||||
plt.savefig(filename+'.jpg', dpi=300)
|
|
||||||
if show == 1:
|
|
||||||
plt.show()
|
|
||||||
plt.close('all')
|
|
||||||
|
|
||||||
|
|
||||||
def plot_3d_surface(x, y, matrix, xlabel='x', ylabel='y', zlabel='z', title='', filename='a', show=1, save=0, z_min=None, z_max=None):
|
|
||||||
import matplotlib.pyplot as plt
|
|
||||||
from matplotlib import cm
|
|
||||||
from matplotlib.ticker import LinearLocator
|
|
||||||
matrix = np.array(matrix)
|
|
||||||
fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
|
|
||||||
plt.subplots_adjust(bottom=0.1, right=0.65)
|
|
||||||
x, y = np.meshgrid(x, y)
|
|
||||||
if len(matrix.shape) == 2:
|
|
||||||
surf = ax.plot_surface(x, y, matrix, cmap=cm.coolwarm, linewidth=0, antialiased=False)
|
|
||||||
elif len(matrix.shape) == 3:
|
|
||||||
for i0 in range(matrix.shape[2]):
|
|
||||||
surf = ax.plot_surface(x, y, matrix[:,:,i0], cmap=cm.coolwarm, linewidth=0, antialiased=False)
|
|
||||||
ax.set_title(title, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
ax.set_xlabel(xlabel, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
ax.set_ylabel(ylabel, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
ax.set_zlabel(zlabel, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
ax.zaxis.set_major_locator(LinearLocator(5))
|
|
||||||
ax.zaxis.set_major_formatter('{x:.2f}')
|
|
||||||
if z_min!=None or z_max!=None:
|
|
||||||
if z_min==None:
|
|
||||||
z_min=matrix.min()
|
|
||||||
if z_max==None:
|
|
||||||
z_max=matrix.max()
|
|
||||||
ax.set_zlim(z_min, z_max)
|
|
||||||
ax.tick_params(labelsize=15)
|
|
||||||
labels = ax.get_xticklabels() + ax.get_yticklabels() + ax.get_zticklabels()
|
|
||||||
[label.set_fontname('Times New Roman') for label in labels]
|
|
||||||
cax = plt.axes([0.80, 0.15, 0.05, 0.75])
|
|
||||||
cbar = fig.colorbar(surf, cax=cax)
|
|
||||||
cbar.ax.tick_params(labelsize=15)
|
|
||||||
for l in cbar.ax.yaxis.get_ticklabels():
|
|
||||||
l.set_family('Times New Roman')
|
|
||||||
if save == 1:
|
|
||||||
plt.savefig(filename+'.jpg', dpi=300)
|
|
||||||
if show == 1:
|
|
||||||
plt.show()
|
|
||||||
plt.close('all')
|
|
||||||
|
|
||||||
|
|
||||||
def plot_contour(x, y, matrix, xlabel='x', ylabel='y', title='', filename='a', show=1, save=0):
|
|
||||||
import matplotlib.pyplot as plt
|
|
||||||
fig, ax = plt.subplots()
|
|
||||||
plt.subplots_adjust(bottom=0.2, right=0.75, left = 0.16)
|
|
||||||
x, y = np.meshgrid(x, y)
|
|
||||||
contour = ax.contourf(x,y,matrix,cmap='jet')
|
|
||||||
ax.set_title(title, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
ax.set_xlabel(xlabel, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
ax.set_ylabel(ylabel, fontsize=20, fontfamily='Times New Roman')
|
|
||||||
ax.tick_params(labelsize=15)
|
|
||||||
labels = ax.get_xticklabels() + ax.get_yticklabels()
|
|
||||||
[label.set_fontname('Times New Roman') for label in labels]
|
|
||||||
cax = plt.axes([0.78, 0.17, 0.08, 0.71])
|
|
||||||
cbar = fig.colorbar(contour, cax=cax)
|
|
||||||
cbar.ax.tick_params(labelsize=15)
|
|
||||||
for l in cbar.ax.yaxis.get_ticklabels():
|
|
||||||
l.set_family('Times New Roman')
|
|
||||||
if save == 1:
|
|
||||||
plt.savefig(filename+'.jpg', dpi=300)
|
|
||||||
if show == 1:
|
|
||||||
plt.show()
|
|
||||||
plt.close('all')
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
# download
|
|
||||||
|
|
||||||
def download_with_scihub(address=None, num=1):
|
|
||||||
from bs4 import BeautifulSoup
|
|
||||||
import re
|
|
||||||
import requests
|
|
||||||
import os
|
|
||||||
if num==1 and address!=None:
|
|
||||||
address_array = [address]
|
|
||||||
else:
|
|
||||||
address_array = []
|
|
||||||
for i in range(num):
|
|
||||||
address = input('\nInput：')
|
|
||||||
address_array.append(address)
|
|
||||||
for address in address_array:
|
|
||||||
r = requests.post('https://sci-hub.st/', data={'request': address})
|
|
||||||
print('\nResponse：', r)
|
|
||||||
print('Address：', r.url)
|
|
||||||
soup = BeautifulSoup(r.text, features='lxml')
|
|
||||||
pdf_URL = soup.iframe['src']
|
|
||||||
if re.search(re.compile('^https:'), pdf_URL):
|
|
||||||
pass
|
|
||||||
else:
|
|
||||||
pdf_URL = 'https:'+pdf_URL
|
|
||||||
print('PDF address：', pdf_URL)
|
|
||||||
name = re.search(re.compile('fdp.*?/'),pdf_URL[::-1]).group()[::-1][1::]
|
|
||||||
print('PDF name：', name)
|
|
||||||
print('Directory：', os.getcwd())
|
|
||||||
print('\nDownloading...')
|
|
||||||
r = requests.get(pdf_URL, stream=True)
|
|
||||||
with open(name, 'wb') as f:
|
|
||||||
for chunk in r.iter_content(chunk_size=32):
|
|
||||||
f.write(chunk)
|
|
||||||
print('Completed!\n')
|
|
||||||
if num != 1:
|
|
||||||
print('All completed!\n')
|
|
||||||
BIN
PyPI/dist/guan-0.0.1-py3-none-any.whl
vendored
BIN
PyPI/dist/guan-0.0.1-py3-none-any.whl
vendored
Binary file not shown.
BIN
PyPI/dist/guan-0.0.1.tar.gz
vendored
BIN
PyPI/dist/guan-0.0.1.tar.gz
vendored
Binary file not shown.
@@ -1,19 +0,0 @@
|
|||||||
Metadata-Version: 2.1
|
|
||||||
Name: guan
|
|
||||||
Version: 0.0.1
|
|
||||||
Summary: An open source python package
|
|
||||||
Home-page: https://py.guanjihuan.com
|
|
||||||
Author: guanjihuan
|
|
||||||
Author-email: guanjihuan@163.com
|
|
||||||
License: UNKNOWN
|
|
||||||
Project-URL: Bug Tracker, https://py.guanjihuan.com
|
|
||||||
Platform: UNKNOWN
|
|
||||||
Classifier: Programming Language :: Python :: 3
|
|
||||||
Classifier: License :: OSI Approved :: MIT License
|
|
||||||
Classifier: Operating System :: OS Independent
|
|
||||||
Requires-Python: >=3.6
|
|
||||||
Description-Content-Type: text/markdown
|
|
||||||
License-File: LICENSE
|
|
||||||
|
|
||||||
GUAN is an open-source python package developed and maintained by https://www.guanjihuan.com. The primary location of this package is on website https://py.guanjihuan.com.
|
|
||||||
|
|
||||||
@@ -1,9 +0,0 @@
|
|||||||
LICENSE
|
|
||||||
README.md
|
|
||||||
pyproject.toml
|
|
||||||
setup.cfg
|
|
||||||
src/guan/__init__.py
|
|
||||||
src/guan.egg-info/PKG-INFO
|
|
||||||
src/guan.egg-info/SOURCES.txt
|
|
||||||
src/guan.egg-info/dependency_links.txt
|
|
||||||
src/guan.egg-info/top_level.txt
|
|
||||||
@@ -1 +0,0 @@
|
|||||||
|
|
||||||
@@ -1 +0,0 @@
|
|||||||
guan
|
|
||||||
Reference in New Issue
Block a user