The second reference state of the open XXZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz. In the quasi-classical limit, two sets of Bethe states give the complete eigenstates of the associated Gaudin model. PACS: 03.65.Fd; 04.20.Jb; 05.30.-d; 75.10.Jm

It has recently been observed that the permanent of a non-negative matrix, i.e., of a matrix containing only nonnegative real entries, can very well be approximated by solving a certain Bethe free energy minimization problem with the help of the sum-product algorithm. We call the resulting approximation of the permanent the Bethe permanent. In this paper we give reasons why this approach to app...

. Note that there are three terms in the expression, one for each edge, one for each factor node, and one for each variable node in the factor graph. The following claim justifies the study of Bethe free energy. Claim 1. For any factor graph, the stationary points of the Bethe free energy correspond to the fixed points of the Belief Propagation algorithm and vice versa. That is, ∂GB ∂ν = 0 if a...

We examine the question of whether Bethe’s ansatz reproduces all states in the periodic Heisenberg XXZ and XXX spin chains. As was known to Bethe himself, there are states for which the Bethe momenta kn diverge: these are in fact the simplest examples of “string” solutions. The coefficients of the Bethe wavefunction, too, diverge. When there are only two down spins in the system (the case consi...

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(n)), Y(gl(m|n)), Ûq(gl(n)) or Ûq(gl(m|n)) (super)algebras, with arbitrary representations (i.e. ‘spins’) on each site of the chain and diagonal boundary matrices (K+(u),K−(u)). The nested Bethe anstaz applies for a general K−(u), but a particular form of the K+(u) matrix. The construction extend...

We compute the eigenfunctions, energies and Bethe equations for a class of generalized integrable Hubbard models based on gl(n|m)⊕ gl(2) superalgebras. The Bethe equations appear to be similar to the Hubbard model ones, up to a phase due to the integration of a subset of ‘simple’ Bethe equations. We discuss relations with AdS/CFT correspondence, and with condensed matter physics.

The Bethe ansatz can be used to compute anomalous dimensions in N = 4 SYM theory. The classical solutions of the sigma-model on AdS5 × S 5 can also be parameterized by an integral equation of Bethe type. In this note the relationship between the two Bethe ansätze is reviewed following hep-th/0402207.

We give a brief review on the use of Bethe ansatz techniques to construct solutions of recursive functional equations which emerged in a bootstrap approach to the quantum Ernst system. The construction involves two particular limits of a rational Bethe ansatz system with complex inhomogeneities. First, we pinch two insertions to the critical value. This links Bethe systems with different number...

We propose the exact S-matrix for the planar limit of the N = 6 super ChernSimons theory recently proposed by Aharony, Bergman, Jafferis, and Maldacena for the AdS4/CFT3 correspondence. Assuming SU(2|2) symmetry, factorizability and certain crossing-unitarity relations, we find the S-matrix including the dressing phase. We use this S-matrix to formulate the asymptotic Bethe ansatz. Our result f...