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

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.