Quenches and dynamical phase transitions in a non-integrable quantum Ising model

TL;DR

This paper investigates the non-equilibrium dynamics and dynamical phase transitions in a non-integrable quantum Ising model under various quench protocols, revealing conditions for the occurrence of DPTs and their relation to ground state changes.

Contribution

It provides a detailed numerical and analytical study of DPTs in a non-integrable quantum Ising model, including the effects of slow and sudden quenches, and maps the model to an effective integrable system for explanation.

Findings

DPTs occur periodically during slow quenches across the QCP.

DPTs can appear or disappear during sudden quenches depending on the initial and final states.

The change in ground state nature influences the presence of DPTs after a sudden quench.

Abstract

We study quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagentic interactions in the presence of a longitudinal field which renders the model non-integrable. The dynamics of the spin chain is studied following a slow (characterized by a rate) or sudden quenches of the longitudinal field; the residual energy, as obtained numerically using a t-DMRG scheme, is found to satisfy analytically predicted scaling relations in both the cases. However, analyzing the temporal evolution of the Loschmidt overlap, we find different possibilities of the presence (or absence) of dynamical phase transitions (DPTs) manifested in the non-analyticities of the rate function. Even though the model is non-integrable, there are {periodic} occurrences of DPTs when the system is slowly ramped across the quantum critical point (QCP) as opposed to the ferromagnetic (FM) version of the model; this numerical finding is qualitatively explained by mapping the original model to an effective integrable spin model which is appropriate for describing such slow quenches. Furthermore, concerning the sudden quenches, our numerical results show that in some cases, DPTs can be present even when the spin chain is quenched within the same phase or even to the QCP while in some other situations they completely disappear even after quenching across the QCP. These observations lead us to the conclusion that it is the change in the nature of the ground state that determines the presence of DPTs following a sudden quench.