Lattice Approach to Excited TBA Boundary Flows: Tricritical Ising Model

TL;DR

This paper develops a lattice-based method to derive TBA equations for boundary flows in the tricritical Ising model, classifying excitations and analyzing their evolution along the RG flow.

Contribution

It introduces a lattice approach to derive boundary TBA equations and classifies excitations for boundary flows in the tricritical Ising model, linking lattice and continuum descriptions.

Findings

Derived TBA equations for boundary excitations.

Classified excitations using (m,n) systems and quantum numbers.

Numerically solved TBA equations to analyze boundary flows.

Abstract

We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering the continuum scaling limit of the A4 lattice model with integrable boundaries. Fixing the bulk weights to their critical values, the integrable boundary weights admit two boundary fields $\xi$ and $\eta$ which play the role of the perturbing boundary fields $\phi_{1,3}$ and $\phi_{1,2}$ inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations.