Out-of-time-order correlations and Floquet dynamical quantum phase transition

TL;DR

This paper demonstrates that out-of-time-order correlators (OTOCs) can effectively probe Floquet dynamical quantum phase transitions (FDQPTs) in exactly solvable Floquet spin models, revealing characteristic decay behaviors and signatures at transition points.

Contribution

It introduces the use of OTOCs to detect FDQPTs in Floquet spin models and uncovers their decay patterns and specific signatures at phase transition boundaries.

Findings

OTOCs signal FDQPT boundaries via global minima of time-averaged correlators.

OTOCs decay algebraically with different exponents in FDQPT and non-FDQPT regions.

Imaginary parts of OTOCs vanish during FDQPT in the synchronized Floquet XY model.

Abstract

Out-of-time-order correlators (OTOCs) progressively play an important role in different fields of physics, particularly in the non-equilibrium quantum many-body systems. In this paper, we show that OTOCs can be used to prob the Floquet dynamical quantum phase transitions (FDQPTs). We investigate the OTOCs of two exactly solvable Floquet spin models, namely: Floquet XY chain and synchronized Floquet XY model. We show that the border of driven frequency range, over which the Floquet XY model shows FDQPT, signals by the global minimum of the infinite-temperature time averaged OTOC. Moreover, our results manifest that OTOCs decay algebraically in the long time, for which the decay exponent in the FDQPT region is different from that of in the region where the system does not show FDQPTs. In addition, for the synchronized Floquet XY model, where FDQPT occurs at any driven frequency depending on the initial condition at infinite or finite temperature, the imaginary part of the OTOCs become zero whenever the system shows FDQPT.