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

TL;DR

This paper provides an exact solution and thermodynamic analysis of a supersymmetric elliptic spin chain, revealing its critical behavior at low temperatures and differences from related models.

Contribution

It presents the first closed-form solution of the su(1|1) elliptic spin chain and its thermodynamic properties, highlighting its relation to free fermions and critical XX behavior.

Findings

Energy levels become normally distributed in the thermodynamic limit.

At low temperatures, the chain behaves as a critical XX model.

The model deviates from the Haldane-Shastry chain in essential ways.

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.