Correlations and dynamical quantum phase transitions in an interacting topological insulator

TL;DR

This paper investigates the relationship between dynamical quantum phase transitions and correlation measures in an interacting topological insulator, revealing how order parameters and correlations behave around DQPTs during quench dynamics.

Contribution

It demonstrates that equilibrium order parameters show signatures near DQPTs and explores how interactions influence correlation decay and buildup in a topological model.

Findings

Order parameters exhibit signatures around DQPTs in short time.

Nearest neighbor correlations decay while further neighbors build up over time.

Inter-cell interactions suppress two-site correlations.

Abstract

Dynamical quantum phase transitions (DQPTs), which refer to the criticality in time of a quantum many-body system, have attracted much theoretical and experimental research interest recently. Despite DQPTs are defined and signalled by the non-analyticities in the Loschmidt rate, its interrelation with various correlation measures such as the equilibrium order parameters of the system remains unclear. In this work, by considering the quench dynamics in an interacting topological model, we find that the equilibrium order parameters of the model in general exhibit signatures around the DQPT, in the short time regime. The first extrema of the equilibrium order parameters are connected to the first Loschmidt rate peak. By studying the unequal-time two-point correlation, we also find that the correlation between the nearest neighbors decays while that with neighbors further away builds up as time grows in the non-interacting case, and upon the addition of repulsive intra-cell interactions. On the other hand, the inter-cell interaction tends to suppress the two-site correlations. These findings could provide us insights into the characteristic of the system around DQPTs, and pave the way to a better understanding of the dynamics in non-equilibrium quantum many-body systems.