Nonlinear integral equations for the finite size effects of RSOS and vertex-models and related quantum field theories

TL;DR

This paper derives nonlinear integral equations from lattice models to accurately describe finite size effects and ground state energies in related quantum field theories, facilitating analysis of excited states.

Contribution

It introduces new two-component nonlinear integral equations for RSOS and vertex models, extending to fractional supersymmetric sine-Gordon models, and confirms their correctness through numerical and analytical checks.

Findings

Equations accurately describe finite size effects in lattice models.

The derived equations simplify the analysis of excited states.

Validation confirms the equations' correctness for various models.

Abstract

Starting from critical RSOS lattice models with appropriate inhomogeneities, we derive two component nonlinear integral equations to describe the finite volume ground state energy of the massive $\phi_{id,id,adj}$ perturbation of the $SU(2)_k \times SU(2)_{k'} /SU(2)_{k+k'}$ coset models. When $k' \to \infty$ while the value of $k$ is fixed, the equations correspond to the current-current perturbation of the $SU(2)_k$ WZW model. Then modifying one of the kernel functions of these equations, we propose two component nonlinear integral equations for the fractional supersymmetric sine-Gordon models. The lattice versions of our equations describe the finite size effects in the corresponding lattice models, namely in the critical RSOS($k,q$) models, in the isotropic higher-spin vertex models, and in the anisotropic higher-spin vertex models. Numerical and analytical checks are also performed to confirm the correctness of our equations. These type of equations make it easier to treat the excited state problem.