We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of the boundary parameters, the Bethe Ansatz solution is formulated in terms of Jacobian elliptic functions.

The Zn elliptic Gaudin model with integrable boundaries specified by generic nondiagonal K-matrices with n+ 1 free boundary parameters is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. PACS: 03.65.Fd; 04.20.Jb; 05.30.-d; 75.10.Jm

The An−1 Gaudin model with integerable boundaries specified by non-diagonal Kmatrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. PACS: 03.65.Fd; 04.20.Jb; 05.30.-d; 75.10.Jm

We consider one-dimensional elliptic Ruijsenaars model of type BC1. It is given by a three-term difference Schrödinger operator L containing 8 coupling constants. We show that when all coupling constants are integers, L has meromorphic eigenfunctions expressed by a variant of Bethe ansatz. This result generalizes the Bethe ansatz formulas known in the A1-case.

Form factors are derived for a model describing the coherent Joseph-son tunneling between two coupled Bose-Einstein condensates. This is achieved by studying the exact solution of the model in the framework of the algebraic Bethe ansatz. In this approach the form factors are expressed through determinant representations which are functions of the roots of the Bethe ansatz equations.

We prove that the disordered Gibbs distribution in the ferromagnetic Ising model on the Bethe lattice is extreme for T^ T?, where TC SG is the critical temperature of the spin glass model on the Bethe lattice, and it is not extreme for T<TC .

We consider one-dimensional elliptic Ruijsenaars model of type BC1. It is given by a three-term difference Schrödinger L operator containing 8 coupling constants. We show that when all coupling constants are integers, L has meromorphic eigenfunctions expressed by a variant of Bethe ansatz. This result generalizes the Bethe ansatz formulas known in the A1-case.

We prove that the Bethe expression for the conditional input-output entropy of cycle LDPC codes on binary symmetric channels above the MAP threshold is exact in the large block length limit. The analysis relies on methods from statistical physics. The finite size corrections to the Bethe expression are expressed through a polymer expansion which is controlled thanks to expander and counting arg...

We study a superconducting integrable model of strongly correlated electrons in 1 + 1 dimensions. We construct all six Bethe Ansätze for the model and give explicit expressions for lowest conservation laws. We also prove a lowest weight theorem for the Bethe-Ansatz states.

– The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within th...