On a Set of Bethe-Ansatz Equetions for Quantium Heisenberg Chains with Elliptic Exchange

The eigenvectors of the Hamiltonian $\mathscr{H}_N$ 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.