Geometry effect of the dynamical quantum phase transitions at finite temperatures

TL;DR

This paper explores how geometric and topological features of dynamical quantum phase transitions are affected by finite temperatures, introducing new concepts like DGOP and analyzing their behavior in various models.

Contribution

It introduces the concepts of parallel quench, DGOP, and extends the DTOP to finite-temperature models, providing new insights into geometric and topological properties of DQPTs.

Findings

DGOP reduces to Pancharatnam phase at zero temperature

Finite temperature disrupts DTOP quantization but preserves transition signatures

Thermal fluctuations influence boundary effects in topological dynamics

Abstract

Dynamical quantum phase transitions (DQPTs) probe the nonequilibrium evolution of quantum systems, unveiling their geometric and topological characteristics. In this study, we introduce the concepts of parallel quench and dynamic geometrical order parameter (DGOP) for non-band models, where these quantities capture the geometric shifts associated with DQPTs. At zero temperature, the DGOP corresponds to the Pancharatnam geometric phase, while at finite temperatures, it extends to the interferometric geometric phase. We further generalize the dynamic topological order parameter (DTOP) to finite-temperature band models, examining its behavior in the Su-Schrieffer-Heeger (SSH) model. Our analysis shows that thermal fluctuations and boundary effects at finite temperatures disrupt the quantization of the DTOP, yet it retains signatures of topological transitions. These findings deepen the understanding of geometric and topological properties in quantum dynamics, illuminating DQPTs across both non-band and band frameworks.