Exact solution and thermodynamics of a spin chain with long-range elliptic interactions

Abstract

We solve in closed form the simplest (su(1|1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions, and on the exact computation of the Fourier transform of the resulting elliptic hopping amplitude. We also compute the thermodynamic functions of the finite (elliptic) chain and their low temperature limit, and show that the energy levels become normally distributed in the thermodynamic limit. Our results indicate that at low temperatures the su(1|1) elliptic chain behaves as a critical XX model, and deviates in an essential way from the Haldane-Shastry chain.

arXiv commentTypeset with LaTeX, 7 figures, 30 pages; considerably enlarged version of previous submission

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Cited by in corpus (8)

• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• A new perspective on the integrability of Inozemtsev's elliptic spin chain
• Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions
• Supersymmetric spin chains with non-monotonic dispersion relation: criticality and entanglement entropy
• Thermodynamics of Inozemtsev's Elliptic Spin Chain
• A novel class of translationally invariant spin chains with long-range interactions
• Supersymmetric $t$-$J$ models with long-range interactions: partition function and spectrum
• Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions