Thermodynamics of the quantum $su(1,1)$ Landau-Lifshitz model

TL;DR

This paper develops the thermodynamics of the quantum su(1,1) Landau-Lifshitz model, deriving Bethe Ansatz equations and analyzing stability, revealing that only negative chemical potentials are permissible and that the model is stable at zero temperature.

Contribution

It introduces a thermodynamic framework for the quantum su(1,1) Landau-Lifshitz model, including the derivation of Bethe Ansatz equations based on self-adjoint extensions.

Findings

Only negative chemical potentials are allowed due to kernel singularities.

The model exhibits no instabilities at zero temperature.

The thermodynamic Bethe Ansatz equations are explicitly derived.

Abstract

We present thermodynamics of the quantum su(1,1) Landau-Lifshitz model, following our earlier exposition [J. Math. Phys. 50, 103518 (2009)] of the quantum integrability of the theory, which is based on construction of self-adjoint extensions, leading to a regularized quantum Hamiltonian for an arbitrary n-particle sector. Starting from general discontinuity properties of the functions used to construct the self-adjoint extensions, we derive the thermodynamic Bethe Ansatz equations. We show that due to non-symmetric and singular kernel, the self-consistency implies that only negative chemical potential values are allowed, which leads to the conclusion that, unlike its su(2) counterpart, the su(1,1) LL theory at T=0 has no instabilities.