Thermodynamics of the Heisenberg XXX chain with negative spin

TL;DR

This paper investigates the thermodynamics of the Heisenberg XXX chain with negative spin, revealing unique vacuum structures, excitation spectra, and phase transitions that differ from the positive spin case, with implications for quantum field theories.

Contribution

It provides the first detailed thermodynamic analysis of the negative spin XXX chain, highlighting its distinct vacuum, excitation spectrum, and low-temperature behavior compared to the conventional model.

Findings

Distinct vacuum structure and excitation spectrum for negative spin

Modified thermodynamic Bethe Ansatz equations and unconventional low-temperature behavior

Identification of a quantum phase transition and Luttinger-liquid like phase

Abstract

We study the thermodynamics of the isotropic Heisenberg XXX spin chain with negative spin, focusing on the case $s=-1$. The model is equivalent to the quantum lattice nonlinear Schr\"odinger (NLS) model and appears as an effective theory in deep inelastic scattering in high-energy quantum chromodynamics. Owing to its integrability, it admits a consistent Bethe Ansatz description and a well-defined thermodynamic limit. Using the thermodynamic Bethe Ansatz, we analyze the ground state, elementary excitations, and finite-temperature properties. In contrast to the conventional positive spin XXX chain, the negative spin model exhibits a distinct vacuum structure and excitation spectrum, leading to modified TBA equations and unconventional low-temperature behavior. Although the integral equations resemble those of the Lieb-Liniger Bose gas, the thermodynamics and scaling properties are qualitatively different and cannot be continuously connected. We derive the free energy, entropy, and specific heat, and identify a quantum phase transition separating different thermodynamic regimes. At zero temperature, the excitation spectrum becomes linear in the continuum limit and can be described by a conformal field theory. The low-temperature regime realizes a Luttinger-liquid like phase with features unique to the negative spin XXX chain.