Topologically driven nonequilibrium phase transitions in diagonal ensembles

Abstract

We identify a new class of topologically driven phase transitions when calculating the Hall conductance of two-band Chern insulators in the long-time limit after a global quench of the Hamiltonian. The Hall conductance is expressed as the integral of the Berry curvature in the diagonal ensemble. Even if the topological invariant of the wave function is conserved under unitary evolution, the Hall conductance as a function of the energy gap in the post-quench Hamiltonian displays a continuous but nonanalytic behavior, that is it has a logarithmically divergent derivative as the gap closes. The coefficient of this logarithmic function is the ratio of the change of Chern number in the ground state of the post-quench Hamiltonian to the energy gap in the initial state. This nonanalytic behavior is universal in two-band Chern insulators.

11 pages, 2 figures, including supplementary materials. In the new version, we generalize our results to a general two-band Chern insulator and provide a strict proof of it

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• Non-equilibrium non-Markovian steady-states in open quantum many-body systems: Persistent oscillations in Heisenberg quantum spin chains
• Universal non-analytic behavior of the non-equilibrium Hall conductance in Floquet topological insulators
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• Topological quantum control: Edge currents via Floquet depinning of skyrmions in the $\nu =0$ graphene quantum Hall antiferromagnet