New Family of Solvable 1D Heisenberg Models

TL;DR

This paper introduces a new family of exactly solvable one-dimensional Heisenberg spin models derived from a Calogero--Sutherland framework, enabling detailed thermodynamic analysis of nonuniform spin chains.

Contribution

It constructs a novel class of solvable 1D Heisenberg models with exchange interactions related to Laguerre polynomial zeros, connecting to known models like Haldane--Shastry.

Findings

Spectrum matches classical 1D Ising chain with nonuniform couplings.

Reproduces Haldane--Shastry and harmonic spin chains by tuning parameters.

Enables thermodynamic study of infinite nonuniform spin chains.

Abstract

Starting from a Calogero--Sutherland model with hyperbolic interaction confined by an external field with Morse potential we construct a Heisenberg spin chain with exchange interaction $\propto 1/\sinh^2 x$ on a lattice given in terms of the zeroes of Laguerre polynomials. Varying the strength of the Morse potential the Haldane--Shastry and harmonic spin chains are reproduced. The spectrum of the models in this class is found to be that of a classical one-dimensional Ising chain with nonuniform nearest neighbour coupling in a nonuniform magnetic field which allows to study the thermodynamics in the limit of infinite chains.