Dynamical Quantum Phase Transitions in Extended Toric-Code Models

TL;DR

This paper investigates dynamical quantum phase transitions in extended toric code models, revealing conditions under which DQPTs occur in both ordered and disordered cases through analysis of Loschmidt overlaps and free-energy density.

Contribution

It demonstrates the occurrence of DQPTs in extended toric code models, including disordered systems, and establishes criteria based on Loschmidt overlaps and initial states.

Findings

DQPTs occur at critical times with nonanalytic free-energy density.

In disordered models, the derivative of the averaged free-energy density signals DQPTs.

Presence of anyonic excitations does not alter DQPT conditions.

Abstract

We study the nonequilibrium dynamics of the extended toric code model (both ordered and disordered) to probe the existence of the dynamical quantum phase transitions (DQPTs). We show that in the case of the ordered toric code model, the zeros of Loschmidt overlap (generalized partition function) occur at critical times when DQPTs occur, which is confirmed by the nonanalyticities in the dynamical counter-part of the free-energy density. Moreover, we show that DQPTs occur for any non-zero field strength if the initial state is the excited state of the toric code model. In the disordered case, we show that it is imperative to study the behavior of the first time derivative of the dynamical free-energy density averaged over all the possible configurations, to characterize the occurrence of a DQPTs in the disordered toric code model since the disorder parameter itself acts as a new artificial dimension. We also show that for the case where anyonic excitations are present in the initial state, the conditions for a DQPTs to occur are the same as what happens in the absence of any excitation.