Nonlinear Integral Equation and Finite Volume Spectrum of Sine-Gordon Theory

TL;DR

This paper investigates the nonlinear integral equation (NLIE) related to sine-Gordon quantum field theory, comparing analytic and numerical predictions to establish NLIE's validity in describing finite size effects.

Contribution

It clarifies the derivation of NLIE from lattice models and proposes a modified quantization rule, enhancing the understanding of sine-Gordon finite volume spectrum.

Findings

Evidence supporting the validity of NLIE for sine-Gordon finite size effects

Necessity to modify the quantization rule for better accuracy

Agreement between NLIE predictions and numerical data

Abstract

We examine the connection between the nonlinear integral equation (NLIE) derived from light-cone lattice and sine-Gordon quantum field theory, considered as a perturbed c=1 conformal field theory. After clarifying some delicate points of the NLIE deduction from the lattice, we compare both analytic and numerical predictions of the NLIE to previously known results in sine-Gordon theory. To provide the basis for the numerical comparison we use data from Truncated Conformal Space method. Together with results from analysis of infrared and ultraviolet asymptotics, we find evidence that it is necessary to change the rule of quantization proposed by Destri and de Vega to a new one which includes as a special case that of Fioravanti et al. This way we find strong evidence for the validity of the NLIE as a description of the finite size effects of sine-Gordon theory.