Finite-size generators for weak integrability breaking perturbations in the Heisenberg chain

TL;DR

This paper investigates the structure of weak integrability-breaking generators in finite Heisenberg chains, revealing relations between different classes and introducing local variants, to better understand slow thermalization in perturbed integrable systems.

Contribution

It provides a systematic analysis of the adiabatic gauge potential in finite systems, establishing relations between generators and proposing local variants for weak perturbations.

Findings

Exact relation between AGPs for boosted and bilocal generators

Boosted generator lacks a closed form but remains quasi-local

Introduction of strictly local weak perturbation variants

Abstract

An integrable model perturbed by special ''weak integrability-breaking'' perturbations thermalizes at timescales much longer than predicted by Fermi's golden rule. Recently, a systematic construction of such perturbations based on the so-called long-range deformations of integrable chains was formulated. These perturbations, obtained as truncations of the long-range deformations in some small parameter expansions, can be viewed as produced by unitary rotations of the short-range integrable models. For infinite systems, several ''generators'' (extensive local, boosted, and bilocal operators) of weak perturbations are known. The main aim of this work is to understand the appropriate generators in finite systems with periodic boundaries since simple counterparts to boosted and bilocal operators are not known in such cases. We approach this by studying the structure of the adiabatic gauge potential (AGP), a proxy for such generators in finite chains, which was originally introduced as a very sensitive measure of quantum chaos. We prove an exact relation between the AGPs for the boosted and bilocal classes of generators and note that the counterpart to boost does not seem to have a closed analytic form in finite systems but shows quasi-locality nonetheless. We also introduce and study strictly local variants of weak integrability-breaking perturbations.