Exact solution and spectral flow for twisted Haldane-Shastry model

TL;DR

This paper provides an exact solution and spectral flow analysis for a twisted Haldane-Shastry spin chain with $1/r^2$ exchange, revealing connections to fractional exclusion statistics and confirming results via the asymptotic Bethe ansatz.

Contribution

It introduces an exact solution for the twisted boundary conditions of the Haldane-Shastry model and characterizes the spectral flow as a function of the twist angle.

Findings

Spectral flow of eigenstates determined exactly

Periodicity of $4\\pi$ for the ground state linked to fractional exclusion statistics

Spectrum reproduces asymptotic Bethe ansatz results

Abstract

The exact solution of the spin chain model with $1/r^2$ exchange is found for twisted boundary conditions. The spectrum thus obtained can be reproduced by the asymptotic Bethe ansatz. The spectral flow of each eigenstate is determined exactly as a function of the twist angle. We find that the period $4\pi$ for the ground state nicely fits in with the notion of fractional exclusion statistics.