A numerical test of the Y-system in the small size limit of the SU(2)x SU(2) Principal Chiral Model

TL;DR

This paper numerically investigates the small size limit of the SU(2) x SU(2) principal chiral model using the Y-system, confirming its predictions and extending the analysis to the ultraviolet region.

Contribution

It provides a numerical validation of the Y-system in the small size limit of the SU(2) x SU(2) principal chiral model, including the development of a relaxed iterative algorithm.

Findings

Numerical access to the deep ultraviolet region L -> 0.

Full agreement with previous TBA computations where possible.

Systematic errors in the numerical method are discussed.

Abstract

Recently, Kazakov, Gromov and Vieira applied the discrete Hirota dynamics to study the finite size spectra of integrable two dimensional quantum field theories. The method has been tested from large values of the size L down to moderate values using the SU(2) x SU(2) principal chiral model as a theoretical laboratory. We continue the numerical analysis of the proposed non-linear integral equations showing that the deep ultraviolet region L -> 0 is numerically accessible. To this aim, we introduce a relaxed iterative algorithm for the numerical computation of the low-lying part of the spectrum in the U(1) sector. We discuss in details the systematic errors involved in the computation. When a comparison is possible, full agreement is found with previous TBA computations.