Thermodynamics of Inozemtsev's Elliptic Spin Chain

Abstract

We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg xxx spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.

36 pages, 12 figures; v2: minor improvements

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• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• The S-matrix of String Bound States
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Cited by in corpus (4)

• Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions
• How coordinate Bethe ansatz works for Inozemtsev model
• How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models
• Hydrodynamics of spin transport in the Haldane-Shastry chain