TBA equations for excited states in the Sine-Gordon model
J. Balog, A. Hegedus
TL;DR
This work derives excited-state Thermodynamic Bethe Ansatz equations for the Sine-Gordon (massive Thirring) theory using a light-cone lattice Bethe Ansatz with twisted boundary conditions that unify even and odd charge sectors. It develops T- and Y-system formalisms, ties them to the Destri–de Vega counting function, and yields continuum finite-volume TBA equations for multi-soliton states with explicit energy and momentum expressions. The infinite-volume solution is obtained explicitly to seed numerical iterations, and extensive comparisons with Destri–de Vega results demonstrate excellent agreement across volumes, including exact results in the A1 case. The methodology clarifies the relation between Y-/T-systems and DdV counting and provides a blueprint for excited-state analyses in other integrable theories.
Abstract
We propose TBA integral equations for multiparticle soliton (fermion) states in the Sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe Ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-deVega equation) description of the model is given.