Dynamical relaxation behavior of extended XY chain with gapless phase following a quantum quench

TL;DR

This paper studies how two-point correlations in extended XY chains relax over time after quantum quenches, revealing different decay behaviors depending on initial states and phases, and maps out dynamical phase diagrams.

Contribution

It demonstrates how additional interactions affect relaxation dynamics in gapless phases and establishes phase diagrams based on relaxation behaviors.

Findings

Relaxation follows t^{-3/2} and t^{-1/2} decay for quenches from gapped phases.

Quenching from gapless phases alters decay to t^{-1} or t^{-1/2} depending on parameters.

Dynamical phase diagrams are constructed based on relaxation behaviors.

Abstract

We investigate the dynamical relaxation behavior of the two-point correlation in extended XY models with a gapless phase after quenches from various initial states. Specifically, we study the XY chain with gapless phase induced by the additional interactions: Dzyaloshinskii-Moriya interaction and XZY-YZX type of three-site interaction. When quenching from the gapped phase, we observe that the additional interactions have no effect on the relaxation behavior. The relaxation behavior is $\delta C_{mn}(t)\sim t^{-3/2}$ and $\sim t^{-1/2}$ for the quench to the commensurate phase and the incommensurate phase, respectively. However, when quenching from the gapless phase, we demonstrate that the scaling behavior of $\delta C_{mn}(t)$ is changed to $\sim t^{-1}$ for the quench to the commensurate phase, and the decay of $\delta C_{mn}(t)$ follows $\sim t^{-1}$ or $\sim t^{-1/2}$ for the quench to the incommensurate phase depending on the parameters of pre-quench Hamiltonian. We also establish the dynamical phase diagrams based on the dynamical relaxation behavior of $\delta C_{mn}(t)$ in the extended XY models.