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The eigenvectors of the Heisenberg Hamiltonian with elliptic form of the exchange spin interaction. (English) Zbl 1362.82009

Summary: The eigenvectors of the Hamiltonian \(\mathcal H_n\) of \(N\)-site 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.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B23 Exactly solvable models; Bethe ansatz
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