We show that the one-dimensional lattice model proposed by Lipatov to describe the high energy scattering of hadrons in multicolor QCD is completely integrable. We identify this model as the XXX Heisenberg chain of noncompact spin s = 0 and find the conservation laws of the model. A generalized Bethe ansatz is developed for the diagonalization of the hamiltonian and for the calculation of hadro...

The one-dimensional Heisenberg XXX spin chain appears in a special limit of the AdS/CFT integrable system. We review various ways of proving its integrability, and discuss the associated methods of solution. In particular, we outline the coordinate and the algebraic Bethe ansatz, giving reference to literature suitable for learning these techniques. Finally, we speculate which of the methods mi...

We study a natural conjecture regarding ferromagnetic ordering of energy levels in the Heisenberg model which complements the Lieb-Mattis Theorem of 1962 for antiferromagnets: for ferromagnetic Heisenberg models the lowest energies in each subspace of fixed total spin are strictly ordered according to the total spin, with the lowest, i.e., the ground state, belonging to the maximal total spin s...

For the sl2 Gaudin model (degenerated quantum integrable XXX spin chain) an exponential generating function of correlators is calculated explicitely. The calculation relies on the Gauss decomposition for the SL2 loop group. From the generating function a new explicit expression for the correlators is derived from which the determinant formulas for the norms of Bethe eigenfunctions due to Richar...

The most general physical boundary S-matrix for the open XXZ spin chain in the non-critical regime (cosh(η) > 1) is derived starting from the bare Bethe ansazt equations. The boundary S-matrix as expected is expressed in terms of Γq-functions. In the isotropic limit corresponding results for the open XXX chain are also reproduced. e-mail: [email protected]

We consider the overlap of Bethe vectors $$XXX$$ spin chain with a diagonal twist and modified general twist. find determinant representation for this under one additional condition on parameters. Such objects arise in calculations nonequilibrium physics.

A bstract We continue the classification of Jordan chains eclectic three state spin chain that we started in our previous article. Following same steps, construct generalised eigenvectors this by computing strongly twisted limit linear combinations a XXX SU(3) chain. show problem can be mapped to computation number positive integer solutions system equations.