The eigenvectors of the Hamiltonian ${\cal H}_{N}$ of $N$ -sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.The eigenvectors of the Hamiltonian ${\cal H}_{N}$ of $N$-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.

arXiv:math-ph/9911022Nov 17, 19992 citations

Static and Dynamic Properties of Random Exchange (S=1/2) Heisenberg Chains

Jorge V. José

Springer proceedings in physicsJan 1, 19860 citations

Critical Behavior of Quantum Heisenberg Chains

P. Schlottmann, Kong-Ju-Bock Lee

Springer proceedings in physicsJan 1, 19901 citation

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

V I Inozemtsev

It is found that the Hamiltonian of the S= 1/2 isotropic Heisenberg chain with N sites and elliptic non-nearest-neighbour exchange is diagonalized in each sector of the Hilbert space with magnetization N/2-M, 1<M<or=(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 Bethe-ansatz-type equations which arise as restrictions on particle pseudomomenta.It is found that the Hamiltonian of the S= 1/2 isotropic Heisenberg chain with N sites and elliptic non-nearest-neighbour exchange is diagonalized in each sector of the Hilbert space with magnetization N/2-M, 1<M<or=(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 Bethe-ansatz-type equations which arise as restrictions on particle pseudomomenta.

arXiv:cond-mat/9504096Journal of Physics A Mathematical and GeneralAug 21, 19955 citations

The eigenvectors of the Hamiltonian

{\cal H}_{N}

N

-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.