Non linear integral equation and excited--states scaling functions in the sine-Gordon model

TL;DR

This paper extends the non-linear integral equation (NLIE) framework to include excited states in the sine-Gordon model, enabling analytical and numerical analysis of its spectrum across different regimes.

Contribution

It generalizes the NLIE to excited states with holes and complex roots, facilitating spectrum calculations in the sine-Gordon/massive Thirring model.

Findings

NLIE applicable to excited states with holes and complex roots

Enables spectrum analysis in large and small L regimes

Provides a basis for numerical computations of excited states

Abstract

The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length $L$ using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large $L$ (perturbative) and small $L$ (conformal) regimes as well as numerically.