Geometric quenches in quantum integrable systems

TL;DR

This paper develops an exact method using the Algebraic Bethe Ansatz to analyze the dynamics of integrable quantum systems after a sudden change in geometry, enabling precise calculations of their nonequilibrium behavior.

Contribution

It introduces a novel exact decomposition technique for initial states post-geometry quench in integrable systems, applicable to models like Lieb-Liniger and Heisenberg chains.

Findings

Provides a framework for calculating time-dependent observables after a geometric quench.

Applicable to a broad class of integrable models.

Enables exact analysis of nonequilibrium dynamics in quantum many-body systems.

Abstract

We consider the generic problem of suddenly changing the geometry of an integrable, one-dimensional many-body quantum system. We show how the physics of an initial quantum state released into a bigger system can be completely described within the framework of the Algebraic Bethe Ansatz, by providing an exact decomposition of the initial state into the eigenstate basis of the system after such a geometric quench. Our results, applicable to a large class of models including the Lieb-Liniger gas and Heisenberg spin chains, thus offer a reliable framework for the calculation of time-dependent expectation values and correlations in this nonequilibrium situation.