Spectrum of a spin chain with inverse square exchange

TL;DR

This paper analyzes the spectrum of an $SU(n)$ spin chain with inverse square exchange interactions, revealing a simple structure with high degeneracy and providing a complete spectrum and thermodynamics for the $SU(2)$ case.

Contribution

It introduces a new exactly solvable spin chain model with inverse square exchange and characterizes its algebraic structure and spectrum.

Findings

Spectrum exhibits highly degenerate super-multiplets.

Identifies the algebraic structure underlying the spectrum.

Provides complete spectrum and thermodynamics for the $SU(2)$ system.

Abstract

The spectrum of a one-dimensional chain of $SU(n)$ spins positioned at the static equilibrium positions of the particles in a corresponding classical Calogero system with an exchange interaction inversely proportional to the square of their distance is studied. As in the translationally invariant Haldane--Shastry model the spectrum is found to exhibit a very simple structure containing highly degenerate ``super-multiplets''. The algebra underlying this structure is identified and several sets of raising and lowering operators are given explicitely. On the basis of this algebra and numerical studies we give the complete spectrum and thermodynamics of the $SU(2)$ system.