Finite temperature dynamical quantum phase transition in a non-Hermitian system

TL;DR

This paper explores how non-Hermiticity and finite temperature influence dynamical quantum phase transitions in a p-wave superconductor, revealing that MSDQPT occurs regardless of gap structure but exhibits different characteristics compared to zero-temperature cases.

Contribution

It demonstrates that MSDQPT persists across phases at finite temperature and analyzes the temperature-dependent evolution of the minimum time for MSDQPT, highlighting differences between gapped and gapless phases.

Findings

MSDQPT occurs regardless of the phase gap structure.

Fisher zeros profile varies between gapped and gapless phases.

Finite temperature washes out half-integer winding number jumps.

Abstract

We investigate the interplay between the non-Hermiticity and finite temperature in the context of mixed state dynamical quantum phase transition (MSDQPT). We consider a $p$-wave superconductor model, encompassing complex hopping and non-Hermiticity that can lead to gapless phases in addition to gapped phases, to examine the MSDQPT and winding number via the intra-phase quench. We find that the MSDQPT is always present irrespective of the gap structure of the underlying phase, however, the profile of Fisher zeros changes between the above phases. Such occurrences of MSDQPT are in contrast to the zero-temperature case where DQPT does not take place for the gapped phase. Surprisingly, the half-integer jumps in winding number at zero-temperature are washed away for finite temperature in the gapless phase. We study the evolution of the minimum time required by the system to experience MSDQPT with the inverse temperature such that gapped and gapless phases can be differentiated. Our study indicates that the minimum time shows monotonic (non-monotonic) behavior for the gapped (gapless) phase.