version 0.0.51

Tutorial/01_test_and_Pauli_matrix.py

@@ -0,0 +1,47 @@
+import guan
+
+# test
+guan.test()
+
+# Pauli matrix
+sigma_0 = guan.sigma_0()
+sigma_x = guan.sigma_x()
+sigma_y = guan.sigma_y()
+sigma_z = guan.sigma_z()
+sigma_00 = guan.sigma_00()
+sigma_0x = guan.sigma_0x()
+sigma_0y = guan.sigma_0y()
+sigma_0z = guan.sigma_0z()
+sigma_x0 = guan.sigma_x0()
+sigma_xx = guan.sigma_xx()
+sigma_xy = guan.sigma_xy()
+sigma_xz = guan.sigma_xz()
+sigma_y0 = guan.sigma_y0()
+sigma_yx = guan.sigma_yx()
+sigma_yy = guan.sigma_yy()
+sigma_yz = guan.sigma_yz()
+sigma_z0 = guan.sigma_z0()
+sigma_zx = guan.sigma_zx()
+sigma_zy = guan.sigma_zy()
+sigma_zz = guan.sigma_zz()
+print('Pauli matrix\n')
+print('sigma_0\n', sigma_0, '\n')
+print('sigma_x\n', sigma_x, '\n')
+print('sigma_y\n', sigma_y, '\n')
+print('sigma_z\n', sigma_z, '\n')
+print('sigma_00\n', sigma_00, '\n')
+print('sigma_0x\n', sigma_0x, '\n')
+print('sigma_0y\n', sigma_0y, '\n')
+print('sigma_0z\n', sigma_0z, '\n')
+print('sigma_x0\n', sigma_x0, '\n')
+print('sigma_xx\n', sigma_xx, '\n')
+print('sigma_xy\n', sigma_xy, '\n')
+print('sigma_xz\n', sigma_xz, '\n')
+print('sigma_y0\n', sigma_y0, '\n')
+print('sigma_yx\n', sigma_yx, '\n')
+print('sigma_yy\n', sigma_yy, '\n')
+print('sigma_yz\n', sigma_yz, '\n')
+print('sigma_z0\n', sigma_z0, '\n')
+print('sigma_zx\n', sigma_zx, '\n')
+print('sigma_zy\n', sigma_zy, '\n')
+print('sigma_zz\n', sigma_zz, '\n')

Tutorial/02_Fourier_transform_and_calculate_band_structures.py.py

@@ -0,0 +1,8 @@
+import guan
+import numpy as np
+
+# Fourier transform / calculate band structures / plot figures
+k_array = np.linspace(-np.pi, np.pi, 100)
+hamiltonian_function = guan.one_dimensional_fourier_transform_with_k(unit_cell=0, hopping=1) # one dimensional chain
+eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
+guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', type='-k')

Tutorial/03_Hamiltonian_of_finite_size_systems.py

@@ -0,0 +1,6 @@
+import guan
+
+# Hamiltonian of finite size
+print('\n', guan.hamiltonian_of_finite_size_system_along_one_direction(3), '\n')
+print(guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(2, 2), '\n')
+print(guan.hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(2, 2, 2), '\n')

Tutorial/04_some_models_in_the_reciprocal_space.py

@@ -0,0 +1,9 @@
+import guan
+import numpy as np
+
+# Hamiltonian of models in the reciprocal space / calculate band structures / plot figures
+k_array = np.linspace(-np.pi, np.pi, 100)
+eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, guan.hamiltonian_of_square_lattice_in_quasi_one_dimension)
+guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', type='-k')
+eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, guan.hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension)
+guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', type='-k')

Tutorial/05_calculate_density_of_states.py

@@ -2,7 +2,7 @@ import guan
 import numpy as np
 
 # calculate density of states
-hamiltonian = guan.finite_size_along_two_directions_for_square_lattice(2,2)
+hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(2,2)
 fermi_energy_array = np.linspace(-4, 4, 400)
 total_dos_array = guan.total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.1)
 guan.plot(fermi_energy_array, total_dos_array, xlabel='E', ylabel='Total DOS', type='-o')
@@ -10,10 +10,10 @@ guan.plot(fermi_energy_array, total_dos_array, xlabel='E', ylabel='Total DOS', t
 fermi_energy = 0
 N1 = 3
 N2 = 4
-hamiltonian = guan.finite_size_along_two_directions_for_square_lattice(N1,N2)
+hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1,N2)
 LDOS = guan.local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2)
 print('square lattice:\n', LDOS, '\n')
-h00 = guan.finite_size_along_one_direction(N2)
+h00 = guan.hamiltonian_of_finite_size_system_along_one_direction(N2)
 h01 = np.identity(N2)
 LDOS = guan.local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00=h00, h01=h01, N2=N2, N1=N1)
 print(LDOS, '\n\n')
@@ -22,10 +22,10 @@ print(LDOS, '\n\n')
 N1 = 3
 N2 = 4
 N3 = 5
-hamiltonian = guan.finite_size_along_three_directions_for_cubic_lattice(N1, N2, N3)
+hamiltonian = guan.hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(N1, N2, N3)
 LDOS = guan.local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2, N3=N3)
 print('cubic lattice:\n', LDOS, '\n')
-h00 = guan.finite_size_along_two_directions_for_square_lattice(N2, N3)
+h00 = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N2, N3)
 h01 = np.identity(N2*N3)
 LDOS = guan.local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3=N3, N2=N2, N1=N1)
 print(LDOS)

Tutorial/06_calculate_conductance_and_scattering_matrix.py

@@ -2,14 +2,12 @@ import guan
 import numpy as np
 
 # calculate conductance
-fermi_energy_array = np.linspace(-5, 5, 400)
-h00 = guan.finite_size_along_one_direction(4)
+fermi_energy_array = np.linspace(-4, 4, 400)
+h00 = guan.hamiltonian_of_finite_size_system_along_one_direction(4)
 h01 = np.identity(4)
 conductance_array = guan.calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01)
-guan.plot(fermi_energy_array, conductance_array, xlabel='E', ylabel='Conductance', type='-o')
+guan.plot(fermi_energy_array, conductance_array, xlabel='E', ylabel='Conductance', type='-')
 
 # calculate scattering matrix
 fermi_energy = 0
-h00 = guan.finite_size_along_one_direction(4)
-h01 = np.identity(4)
 guan.print_or_write_scattering_matrix(fermi_energy, h00, h01)

Tutorial/07_calculate_Chern_number_and_Wilson_loop.py

@@ -0,0 +1,13 @@
+import guan
+import numpy as np
+from math import *
+
+# calculate Chern number
+chern_number = guan.calculate_chern_number_for_square_lattice(guan.hamiltonian_of_one_QAH_model, precision=100)
+print('\nChern number=', chern_number)
+
+# calculate Wilson loop
+wilson_loop_array = guan.calculate_wilson_loop(guan.hamiltonian_of_ssh_model)
+print('Wilson loop =', wilson_loop_array)
+p = np.log(wilson_loop_array)/2/pi/1j
+print('p =', p, '\n')

Tutorial/Fourier_transform_and_calculate_band_structures.py.py

@@ -1,9 +0,0 @@
-import guan
-import numpy as np
-import functools
-
-# Fourier transform / calculate band structures / plot figures
-x_array = np.linspace(-np.pi, np.pi, 100)
-hamiltonian_function = functools.partial(guan.one_dimensional_fourier_transform, unit_cell=0, hopping=1)
-eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function)
-guan.plot(x_array, eigenvalue_array, xlabel='k', ylabel='E', type='-k')

Tutorial/Hamiltonian_of_finite_size_systems.py

@@ -1,6 +0,0 @@
-import guan
-
-# Hamiltonian of finite size
-print(guan.finite_size_along_one_direction(3), '\n')
-print(guan.finite_size_along_two_directions_for_square_lattice(2, 2), '\n')
-print(guan.finite_size_along_three_directions_for_cubic_lattice(2, 2, 2), '\n')

Tutorial/calculate_Chern_number_and_Wilson_loop.py

@@ -1,24 +0,0 @@
-import guan
-import numpy as np
-from math import *
-
-# calculate Chern number
-def hamiltonian_function(kx, ky):  # one QAH model with chern number 2
-    t1 = 1.0
-    t2 = 1.0
-    t3 = 0.5
-    m = -1.0
-    hamiltonian = np.zeros((2, 2), dtype=complex)
-    hamiltonian[0, 1] = 2*t1*cos(kx)-1j*2*t1*cos(ky)
-    hamiltonian[1, 0] = 2*t1*cos(kx)+1j*2*t1*cos(ky)
-    hamiltonian[0, 0] = m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky)
-    hamiltonian[1, 1] = -(m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky))
-    return hamiltonian
-chern_number = guan.calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100)
-print('Chern number=', chern_number)
-
-# calculate Wilson loop
-wilson_loop_array = guan.calculate_wilson_loop(guan.hamiltonian_of_ssh_model)
-print('Wilson loop =', wilson_loop_array)
-p = np.log(wilson_loop_array)/2/pi/1j
-print('p =', p, '\n')

Tutorial/some_models_in_the_reciprocal_space.py

@@ -1,9 +0,0 @@
-import guan
-import numpy as np
-
-# Hamiltonian of models in the reciprocal space / calculate band structures / plot figures
-x_array = np.linspace(-np.pi, np.pi, 100)
-eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(x_array, guan.hamiltonian_of_square_lattice_in_quasi_one_dimension)
-guan.plot(x_array, eigenvalue_array, xlabel='k', ylabel='E', type='-k')
-eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(x_array, guan.hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension)
-guan.plot(x_array, eigenvalue_array, xlabel='k', ylabel='E', type='-k')

Tutorial/test_and_Pauli_matrix.py

@@ -1,12 +0,0 @@
-import guan
-
-# test
-print('test')
-guan.test()
-
-# Pauli matrix
-print('Pauli matrix')
-print('sigma_0:\n', guan.sigma_0(), '\n')
-print('sigma_x:\n', guan.sigma_x(), '\n')
-print('sigma_y:\n', guan.sigma_y(), '\n')
-print('sigma_z:\n', guan.sigma_z(), '\n')