Bethe Algebra of Homogeneous XXX Heisenberg Model has Simple Spectrum

Bethe Algebra of Homogeneous Xxx Heisenberg Model Has Simple Spectrum

We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional gl 2 -modules. As a byproduct we show that there exist exactly ( n l )

Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz

We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this r...

Ansatz Equations in the XXX - Heisenberg Model

We study the equations for the quasi-momenta which characterize the wave-functions in the Bethe ansatz for the XXX-Heisenberg model. We show in a simple analytical fashion, that the usual " string hypothesis " incorrectly predicts the number of real solutions and the 1

Singularities in the Bethe solution of the XXX and XXZ Heisenberg spin chains

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...

Heisenberg Model, Bethe Ansatz, and Random Walks