Critical properties of Sudden Quench Dynamics in the anisotropic XY Model

TL;DR

This paper investigates the critical behavior of the anisotropic XY model under sudden quenches, revealing how dynamical quantum phase transitions can be characterized by susceptibility and correlation derivatives, with critical exponents and long-range correlations analyzed.

Contribution

It provides a theoretical analysis of dynamical quantum phase transitions in the XY model, highlighting the roles of magnetic susceptibility and correlation functions as indicators.

Findings

Divergence of quench magnetic susceptibility at critical points.

Identification of critical exponents for dynamical QPT.

Analysis of long-range correlations post-quench.

Abstract

We study the zero temperature quantum dynamical critical behavior of the anisotropic XY chain under a sudden quench in a transverse field. We demonstrate theoretically that both quench magnetic susceptibility and two-particle quench correlation can be used to describe the dynamical quantum phase transition (QPT) properties. Either the quench magnetic susceptibility or the derivative of correlation functions as a function of initial magnetic field $a$ exhibits a divergence at the critical points when final magnetic field $b$ is fixed. A special case that final magnetic field $b$ is just at the critical point is discussed separately. Some of the critical exponents of the dynamical QPT are obtained and the long-range correlation of the quench system is analyzed. We also compare our result with that of the static QPT.