Dynamical quantum phase transition in quantum spin chains with gapless phases

TL;DR

This paper investigates dynamical quantum phase transitions in quantum spin chains with gapless phases, deriving general conditions and analyzing specific models to understand when DQPTs occur or are absent after a quench.

Contribution

It provides a general expression for the Loschmidt echo in systems with asymmetric spectra and explores the conditions for DQPTs in gapless and gapped phase quenches.

Findings

DQPTs may not occur when quenching across quantum phase transitions from gapless to gapped phases.

DQPTs always occur when quenching from gapped to gapped phases.

Different mechanisms explain the absence of DQPTs in certain quenches.

Abstract

The dynamical quantum phase transitions (DQPTs) in quantum spin chains with gapless phases after a sudden quench are studied. We mainly consider the general systems with asymmetrical quasiparticle excitation spectra and obtain the general expression of the Loschmidt echo as well as the general conditions for the occurrence of DQPTs. As two examples, we study the DQPTs in the \emph{XY} chains with Dzyaloshinskii-Moriya interaction and \emph{XZY-YZX} type of three-site interaction. It's found that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Besides, we also analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase.