TCSA and the finite volume boundary state

TL;DR

This paper introduces a novel method for calculating boundary state overlaps in finite volume using the truncated conformal space approach, validated analytically and numerically in specific models, and explores the structure of asymptotic overlaps.

Contribution

It presents a new technique for overlap calculations in finite volume boundary states within the TCSA framework, supported by analytical and numerical validation.

Findings

Validated in the thermally perturbed Ising model

Numerical results in the scaling Lee-Yang model match analytical continuation methods

Proposed a simple argument for asymptotic overlap structure involving Gaudin determinants

Abstract

We develop a new way to calculate the overlap of a boundary state with a finite volume bulk state in the truncated conformal space approach. We check this method in the thermally perturbed Ising model analytically, while in the scaling Lee-Yang model numerically by comparing our results to excited state g-functions, which we obtained by the analytical continuation method. We also give a simple argument for the structure of the asymptotic overlap between the finite volume boundary state and a periodic multiparticle state, which includes the ratio of Gaudin type determinants.