Finite-Volume Spectra of the Lee-Yang Model

TL;DR

This paper analyzes the finite-volume spectra of the non-unitary Lee-Yang model in various geometries, applying integrable perturbations and deriving TBA equations to describe the spectrum and excitations.

Contribution

It derives new TBA equations for the Lee-Yang model with boundaries, defects, and bulk perturbations, confirming previous conjectures and extending understanding of its finite-size spectrum.

Findings

Derived TBA equations for all geometries and excitations.

Confirmed conjectured transmission factors for defects.

Classified excitations using (m,n) systems.

Abstract

We consider the non-unitary Lee-Yang minimal model ${\cal M}(2,5)$ in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels $(r,s)=(1,1),(1,2)$, (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply $\varphi_{1,3}$ integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a $\Phi_{1,3}$ integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated $A_{4}$ RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of $(m,n)$ systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.