Exact (d)->(+)&(-) boundary flow in the tricritical Ising model

TL;DR

This paper derives exact TBA equations for boundary flows in the tricritical Ising model, revealing how degenerate boundary conditions evolve into superpositions of Cardy states and connecting lattice models to conformal sectors.

Contribution

It extends TBA analysis to boundary flows involving superpositions of states and introduces a lattice model realization of these boundary conditions.

Findings

Derived exact TBA equations for excited states.

Described non-Cardy boundary sectors as scaling limits.

Provided the first lattice model example of superimposed Virasoro characters.

Abstract

The integrable perturbation of the degenerate boundary condition (d) by the $\phi_{1,3}$ boundary field generates a renormalization group flow down to the superposition of Cardy boundary states (+)&(-). Exact Thermodynamic Bethe Ansatz (TBA) equations for all the excited states are derived here extending the results of a previous paper to this case. As an intermediate step, the non-Cardy boundary conformal sector (+)&(-) is also described as the scaling limit of an A_4 lattice model with appropriate integrable boundary conditions and produces the first example of superposition of finitized Virasoro characters.