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.

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

References in corpus (6)

• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
• Statistical Phases and Momentum Spacings for One-Dimensional Anyons
• Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
• The Berry-Tabor conjecture for spin chains of Haldane-Shastry type
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• A new perspective on the integrability of Inozemtsev's elliptic spin chain

Cited by in corpus (3)

• A new perspective on the integrability of Inozemtsev's elliptic spin chain
• Supersymmetric spin chains with non-monotonic dispersion relation: criticality and entanglement entropy
• Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions