Universal nonanalytic behavior of the Hall conductance in a Chern insulator at the topologically driven nonequilibrium phase transition

TL;DR

This paper investigates the nonanalytic behavior of Hall conductance in Chern insulators after a quench, revealing a universal topologically driven phase transition characterized by a logarithmic divergence in conductance derivatives.

Contribution

It introduces a universal nonanalytic behavior of Hall conductance at a topological phase transition in quenched Chern insulators, linking it to the winding number of the Green's function.

Findings

Hall conductance exhibits nonanalyticity at the transition point

Derivative of conductance with respect to energy gap diverges logarithmically

Universal behavior across various two-band Chern insulators

Abstract

We study the Hall conductance of a Chern insulator after a global quench of the Hamiltonian. The Hall conductance in the long time limit is obtained by applying the linear response theory to the diagonal ensemble. It is expressed as the integral of the Berry curvature weighted by the occupation number over the Brillouin zone. We identify a topologically driven nonequilibrium phase transition, which is indicated by the nonanalyticity of the Hall conductance as a function of the energy gap m_f in the post-quench Hamiltonian H_f. The topological invariant for the quenched state is the winding number of the Green's function W, which equals the Chern number for the ground state of H_f. In the limit that m_f goes to zero, the derivative of the Hall conductance with respect to m_f is proportional to ln(|m_f|), with the constant of proportionality being the ratio of the change of W at m_f = 0 to the energy gap in the initial state. This nonanalytic behavior is universal in two-band Chern insulators such as the Dirac model, the Haldane model, or the Kitaev honeycomb model in the fermionic basis.