Exactly solvable D_N-type quantum spin models with long-range interaction

TL;DR

This paper derives exact spectra for D_N-type Calogero spin models, computes the partition function of the associated spin chain, and analyzes its spectral statistical properties, providing insights into long-range quantum interactions.

Contribution

It presents the first exact solution for D_N-type Calogero spin models and their associated spin chains, including spectral degeneracies and statistical analysis.

Findings

Exact spectra and degeneracies derived for D_N-type models

Partition function computed for the D_N-type spin chain

Spectral properties such as level density and spacing distribution analyzed

Abstract

We derive the spectra of the D_N-type Calogero (rational) su(m) spin model, including the degeneracy factors of all energy levels. By taking the strong coupling limit of this model, in which its spin and dynamical degrees of freedom decouple, we compute the exact partition function of the su(m) Polychronakos-Frahm spin chain of D_N type. With the help of this partition function we study several statistical properties of the chain's spectrum, such as the density of energy levels and the distribution of spacings between consecutive levels.