Dynamical quantum phase transition from a critical quantum quench

TL;DR

This paper investigates dynamical quantum phase transitions during critical quantum quenches, revealing unconventional topological invariants and highlighting the need for revised definitions in critical regimes.

Contribution

It uncovers the behavior of dynamical topological order parameters and Chern numbers at critical points, challenging existing definitions and proposing the influence of singularities.

Findings

Half-quantized or unquantized topological invariants at critical points

Restoration of integer invariants when both Hamiltonians are critical

Singularity of the Bogoliubov angle is key to topological behavior

Abstract

We study the dynamical quantum phase transition of the critical quantum quench, in which the prequenched Hamiltonian, or the postquenched Hamiltonian, or both of them are set to be the critical points of equilibrium quantum phase transitions, we find half-quantized or unquantized dynamical topological order parameter and dynamical Chern number; these results and also the existence of dynamical quantum phase transition are all closely related to the singularity of the Bogoliubov angle at the gap-closing momentum. The effects of the singularity may also be canceled out if both the prequenched and postquenched Hamiltonians are critical, then the dynamical topological order parameter and dynamical Chern number restore to integer ones. Our findings show that the widely accepted definitions of dynamical topological order parameter and dynamical Chern number are problematic for the critical quenches in the perspective of topology, which call for new definitions of them.