Excited State TBA for the $\phi_{2,1}$ perturbed $M_{3,5}$ model

TL;DR

This paper investigates excited state energies in a non-unitary integrable quantum field theory derived from a perturbed minimal conformal model, using TBA equations and numerical comparisons.

Contribution

It derives TBA-like integral equations for excited states in the $ ext{TBA}$ framework for the $ ext{M}_{3,5}$ model perturbed by $ ext{phi}_{2,1}$, linking lattice models to quantum field theory.

Findings

Derived explicit TBA equations for ground and excited states.

Numerical energy gap results agree with TCSA calculations.

Established correspondence between lattice models and IQFT for excited states.

Abstract

We examine some excited state energies in the non-unitary integrable quantum field theory obtained from the perturbation of the minimal conformal field theory model $M_{3,5}$ by its operator $\phi_{2,1}$. Using the correspondence of this IQFT to the scaling limit of the dilute $A_2$ lattice model (in a particular regime) we derive the functional equations for the QFT commuting transfer matrices. These functional equations can be transformed to a closed set of TBA-like integral equations which determine the excited state energies in the finite-size system. In particular, we explicitly construct these equations for the ground state and two lowest excited states. Numerical results for the associated energy gaps are compared with those obtained by the truncated conformal space approach (TCSA).