Z2Pack June 2019

z2pack@lists.phys.ethz.ch

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Help regarding chern number calculation
by MS. PRIYANKA SINHA 01 Jun '19

01 Jun '19

Dear Sir, I am a new user of z2 pack and trying to calculate chern number following the journal https://journals.aps.org/prb/pdf/10.1103/PhysRevB.85.115439 . I have defined the Hamiltonian as given in equation 14. I should get non-zero chern number. But instead of that I am getting zero. I am attaching my code below. Kindly help me in this regard. ********************************************************************* #!/usr/bin/env python # -*- coding: utf-8 -*- # # Author: Dominik Gresch <greschd(a)gmx.ch> # Date: 16.08.2016 14:25:39 CEST # File: haldane.py import json import logging import z2pack import numpy as np import matplotlib.pyplot as plt from numpy import linalg as LA logging.getLogger('z2pack').setLevel(logging.WARNING) # defining pauli matrices identity = np.identity(2, dtype=complex) pauli_x = np.array([[0, 1], [1, 0]], dtype=complex) pauli_y = np.array([[0, -1j], [1j, 0]], dtype=complex) pauli_z = np.array([[1, 0], [0, -1]], dtype=complex) Sx= 1./2. * np.array([[0, 1], [1, 0]], dtype=complex) Sy= 1./2. * np.array([[0, -1j], [1j, 0]], dtype=complex) Sz= 1./2. * np.array([[1, 0], [0, -1]], dtype=complex) def Hamilton(k, m, t1, VR): kx, ky,_= k H = (3. *t1 /2. * ( pauli_x * kx + pauli_y * ky)) * identity H += (3. *t1 /2. * (- pauli_x * kx + pauli_y * ky)) * identity H += 3. *VR /2. * ( pauli_x * Sy - pauli_y * Sx) H += 3. *VR /2. * (- pauli_x * Sy - pauli_y * Sx) #H3 = n * 3. *sqrt3 * t2 * pauli_z *Sz H += (m * Sz) * identity #H5 = u * pauli_z * identity return H def get_chern( m, t1, VR, **settings): system = z2pack.hm.System(lambda k: Hamilton(k, m, t1, VR), bands=1) result = z2pack.surface.run(system=system, surface=lambda t1, t2: [t1, t2, 1], **settings) return z2pack.invariant.chern(result) if __name__ == "__main__": # Task a) print(get_chern(0.3, 1., 0.5 )) #print(get_chern(0.5, 1., 1. / 3., -0.5 * np.pi)) #print(Hamilton(0.1, 1, 0.3,0.5)) ******************************************************************** Thanking You, Priyanka Sinha IIT Guwahati Research Scholar

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Z2Pack June 2019