Abstract
We identify a new class of 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 Chern number of the unitarily-evolving wave function is conserved, 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 the Chern number for 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.
Highlights
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 wave function follows a unitary time evolution, while the local observables in the long time limit settle to the prediction of the diagonal ensemble [14], which in some cases can be reduced to a thermal ensemble or a generalized Gibbs ensemble [15, 16]
The discrepancy in the symmetry protected topological (SPT) order obtained from the Chern number and the Hall conductance is attributed to the fact that the latter must be calculated from the diagonal ensemble, in which the coherence between different eigenstates of Hf in the wave function is lost in the long-time limit
Summary
Pei Wang1, 2, ∗ and Stefan Kehrein1 1Institute for Theoretical Physics, Georg-August-Universitat Gottingen, Friedrich-Hund-Platz 1, Gottingen 37077, Germany 2Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China (Dated: January 15, 2021). The discrepancy in the SPT order obtained from the Chern number (based on unitary time evolution) and the Hall conductance is attributed to the fact that the latter must be calculated from the diagonal ensemble, in which the coherence between different eigenstates of Hf in the wave function is lost in the long-time limit. In this experimentally relevant sense the SPT order of quenched states depends on Hf. Real-time dynamics of the Chern number.– The Hamiltonian of a two-band Chern insulator in two dimensions is expressed as
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