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

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) over cap (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) over cap (f). In the limit m(f) -> 0, the derivative of the Hall conductance with respect to m(f) is proportional to ln vertical bar m(f)vertical bar, 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.