On the spectrum of S=1/2 XXX Heisenberg chain with elliptic exchange

TL;DR

This paper analyzes the spectrum of an S=1/2 Heisenberg chain with elliptic exchange, revealing a novel diagonalization method using solutions to a quantum Calogero-Moser problem and Bethe-ansatz equations.

Contribution

It introduces a new approach to diagonalize the elliptic exchange Heisenberg chain using double quasiperiodic solutions and transcendental Bethe-ansatz equations.

Findings

Spectrum determined by solutions to transcendental equations.

Diagonalization achieved via quantum Calogero-Moser solutions.

Provides explicit characterization of highest-weight states.

Abstract

It is found that the Hamiltonian of S=1/2 isotropic Heisenberg chain with $N$ sites and elliptic non-nearest-neighbor exchange is diagonalized in each sector of the Hilbert space with magnetization $N/2-M$, $1<M\leq[N/2]$, by means of double quasiperiodic meromorphic solutions to the $M$-particle quantum Calogero-Moser problem on a line. The spectrum and highest-weight states are determined by the solutions of the systems of transcendental equations of the Bethe-ansatz type which arise as restrictions to particle pseudomomenta.