Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model

TL;DR

This paper derives a set of nonlinear integral equations for analyzing the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model, enabling efficient numerical evaluation at various temperatures and revealing complex phase behavior.

Contribution

The authors develop a new finite set of NLIE for the sl(4) model, extending previous work and allowing low-temperature analysis without numerical issues.

Findings

Numerical evaluation of the NLIE at finite temperature and chemical potentials.

Identification of critical fields from the zero-temperature limit.

Observation of divergences and logarithmic singularities in magnetic susceptibility.

Abstract

We derive a finite set of nonlinear integral equations (NLIE) for the thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model. Our NLIE can be evaluated numerically for arbitrary finite temperature and chemical potentials. We recover the NLIE for sl(3) as a limiting case. In comparison to other recently derived NLIE, the evaluation at low temperature poses no problem in our formulation. The model shows a rich ground-state phase diagram. We obtain the critical fields from the T to zero limit of our NLIE. As an example for the application of the NLIE, we give numerical results for the SU(4) spin-orbital model. The magnetic susceptibility shows divergences at critical fields in the low-temperature limit and logarithmic singularities for zero magnetic field.