What is an integrable quench?

TL;DR

This paper introduces a definition of integrable initial states for quantum quenches in lattice models, linking them to boundary conditions and providing a method to test their integrability, with applications to various models including XXZ chains.

Contribution

It proposes a new definition of integrable initial states based on local conserved charges and offers an efficient testing method, connecting quantum quenches to boundary conditions in integrable models.

Findings

Integrable states include two-site product states and matrix product states.

All analytically solvable quenches involve integrable initial states.

The method applies to models like XXZ spin chains.

Abstract

Inspired by classical results in integrable boundary quantum field theory, we propose a definition of integrable initial states for quantum quenches in lattice models. They are defined as the states which are annihilated by all local conserved charges that are odd under space reflection. We show that this class includes the states which can be related to integrable boundary conditions in an appropriate rotated channel, in loose analogy with the picture in quantum field theory. Furthermore, we provide an efficient method to test integrability of given initial states. We revisit the recent literature of global quenches in several models and show that, in all of the cases where closed-form analytical results could be obtained, the initial state is integrable according to our definition. In the prototypical example of the XXZ spin-s chains we show that integrable states include two-site product states but also larger families of matrix product states with arbitrary bond dimension. We argue that our results could be practically useful for the study of quantum quenches in generic integrable models.