Thermalization of long range Ising model in different dynamical regimes: a full counting statistics approach

TL;DR

This paper investigates how long-range interactions in the transverse field Ising model affect thermalization after a quantum quench, using full counting statistics and tensor network simulations across different dynamical regimes.

Contribution

It introduces a comprehensive analysis of thermalization in long-range Ising models using full counting statistics and MPS-based methods, highlighting the role of confinement in thermalization behavior.

Findings

Thermalization is suppressed in the strong confinement regime.

Thermalization occurs in the weak confinement regime.

The study maps the dependence of thermalization on interaction range and confinement.

Abstract

We study thermalization of transverse field Ising chain with power law decaying interaction $\sim 1/r^{\alpha}$ following a global quantum quench of the transverse field to two different dynamical regimes. We quantify the thermalization behavior by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the Gibbs canonical ensemble (GCE). To this end, we use matrix product state (MPS) based time dependent variational principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all the interaction strength $\alpha$ considered whereas thermalization occurs in the region with weak confinement.