Initial states in integrable quantum field theory quenches from an integral equation hierarchy

TL;DR

This paper develops an integral equation hierarchy to determine initial states in integrable quantum field theory quenches, providing theoretical and numerical evidence that a squeezed coherent state Ansatz accurately describes the post-quench state.

Contribution

It introduces an integral equation hierarchy based on form factors to determine initial states and proposes an iterative numerical method to solve it, supporting the squeezed coherent state Ansatz.

Findings

The Ansatz closely approximates the solution of the hierarchy.

Numerical solutions validate the theoretical predictions.

The method applies to quenches in Sinh-Gordon theory.

Abstract

We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions deter- mining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provide a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.