TBA and TCSA with boundaries and excited states

TL;DR

This paper investigates the finite-size spectrum of the scaling Lee-Yang model with boundaries using both the truncated conformal space approach and boundary thermodynamic Bethe ansatz, proposing new reflection factors and equations for excited states.

Contribution

It introduces a new family of reflection factors for boundary conditions and revises existing equations for the spectrum, including excited states, with validation against numerical data.

Findings

Identified boundary flows in massless bulk regimes.

Discovered boundary bound states in massive regimes.

Proposed non-minimal reflection factors matching boundary conditions.

Abstract

We study the spectrum of the scaling Lee-Yang model on a finite interval from two points of view: via a generalisation of the truncated conformal space approach to systems with boundaries, and via the boundary thermodynamic Bethe ansatz. This allows reflection factors to be matched with specific boundary conditions, and leads us to propose a new (and non-minimal) family of reflection factors to describe the one relevant boundary perturbation in the model. The equations proposed previously for the ground state on an interval must be revised in certain regimes, and we find the necessary modifications by analytic continuation. We also propose new equations to describe excited states, and check all equations against boundary truncated conformal space data. Access to the finite-size spectrum enables us to observe boundary flows when the bulk remains massless, and the formation of boundary bound states when the bulk is massive.