Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems

TL;DR

This paper demonstrates that by applying a magnetic flux under twist boundary conditions, exact zeros of the Loschmidt echo can be achieved in finite-size quantum systems, revealing dynamical quantum phase transitions through divergent rate functions.

Contribution

It introduces a method to realize dynamical singularities in finite-size systems by tuning magnetic flux, enabling detection of quantum phase transitions without relying on thermodynamic limits.

Findings

Exact zeros of the Loschmidt echo can be achieved in finite systems with flux tuning.

Divergent rate functions occur at critical times when crossing phase transition points.

Critical times are independent of system size, facilitating experimental detection.

Abstract

The dynamical quantum phase transition is characterized by the emergence of nonanalytic behaviors in the rate function, corresponding to the occurrence of exact zero points of the Loschmidt echo in the thermodynamical limit. In general, exact zeros of the Loschmidt echo are not accessible in a finite-size quantum system except for some fine-tuned quench parameters. In this work, we study the realization of the dynamical singularity of the rate function for finite-size systems under the twist boundary condition, which can be introduced by applying a magnetic flux. By tuning the magnetic flux, we illustrate that exact zeros of the Loschmidt echo can be always achieved when the postquench parameter is across the underlying equilibrium phase transition point, and thus the rate function of a finite-size system is divergent at a series of critical times. We demonstrate our theoretical scheme by calculating the Su-Schrieffer-Heeger model and the Creutz model in detail and exhibit its applicability to more general cases. Our result unveils that the emergence of dynamical singularity in the rate function can be viewed as a signature for detecting dynamical quantum phase transition in finite-size systems. We also unveil that the critical times in our theoretical scheme are independent on the systems size, and thus it provides a convenient way to determine the critical times by tuning the magnetic flux to achieve the dynamical singularity of the rate function.