Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange

TL;DR

This paper derives the exact spectrum and partition function of an SU(n) spin chain with inverse-square exchange, revealing equidistant energy levels, high degeneracy, and a q-deformed polynomial structure.

Contribution

It provides the exact solution for the spectrum and partition function of an SU(n) spin chain with inverse-square interactions, including a novel classification of states.

Findings

Energy levels are equidistant with high degeneracy.

Partition function expressed as a q-deformed polynomial.

System described by an effective parafermionic Hamiltonian.

Abstract

The spectrum and partition function of a model consisting of SU(n) spins positioned at the equilibrium positions of a classical Calogero model and interacting through inverse-square exchange are derived. The energy levels are equidistant and have a high degree of degeneracy, with several SU(n) multiplets belonging to the same energy eigenspace. The partition function takes the form of a q-deformed polynomial. This leads to a description of the system by means of an effective parafermionic hamiltonian, and to a classification of the states in terms of "modules" consisting of base-n strings of integers.