Analytic proof of the Sutherland conjecture

TL;DR

This paper provides an analytic proof of the Sutherland conjecture by deriving the spectrum of a Lax matrix for a specific particle system using advanced mathematical techniques.

Contribution

It offers the first rigorous analytic proof of the Sutherland conjecture, connecting the spectrum to the asymptotic Bethe ansatz in the thermodynamic limit.

Findings

Spectrum of the Lax matrix matches the asymptotic Bethe ansatz

Analytic proof confirms the Sutherland conjecture

Uses integral representation of elliptic theta function inverse

Abstract

Using the integral representation of the inverse of the logarithmic derivative of the elliptic theta function, the spectrum of the Lax matrix for the 1D system of particles interacting via inverse sinh-squared potential is shown to be given by the asymptotic Bethe ansatz in the thermodynamic limit.