Thermodynamics of the Heisenberg XXX chain with negative spin
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arXiv
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| Format: | Preprint |
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2026
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| author | Zhong, Rong Chen, Yang-Yang Hao, Kun Yang, Wen-li Korepin, Vladimir |
| author_facet | Zhong, Rong Chen, Yang-Yang Hao, Kun Yang, Wen-li Korepin, Vladimir |
| contents | 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 Schrödinger (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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03714 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thermodynamics of the Heisenberg XXX chain with negative spin Zhong, Rong Chen, Yang-Yang Hao, Kun Yang, Wen-li Korepin, Vladimir High Energy Physics - Theory Statistical Mechanics Quantum Physics 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 Schrödinger (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. |
| title | Thermodynamics of the Heisenberg XXX chain with negative spin |
| topic | High Energy Physics - Theory Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2602.03714 |