H.E. Boos1 Institute for High Energy Physics Protvino, 142284, Russia V.E. Korepin 2 C.N. Yang Institute for Theoretical Physics State University of New York at Stony Brook Stony Brook, NY 11794{3840, USA Abstract Riemann zeta function is an important object of number theory. We argue that it is related to Heisenberg spin 1/2 anti-ferromagnet. In the XXX spin chain we study the probability of f...

In these lectures the introduction to algebraic aspects of Bethe Ansatz is given. The applications to the seminal spin 1/2 XXX model is discussed in detail and the generalization to higher spin as well as XXZ and lattice Sine-Gordon model are indicated. The origin of quantum groups and their appearance in CFT models is explained. The text can be considered as a guide to the research papers in t...

the entanglement at zero-temperature is studied in a two-qubit xz spin-1/2 chain model in anexternal magnetic field which is applied in the z direction. we have obtained an analytical relation forthe effect of the external magnetic field on the concurrence. it is shown that the ground state of thesystem depends on the strength of exchange coupling. we have shown that the analytical relation oft...

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in framework of quantum inverse scattering method. Following algebraic Bethe ansatz diagonalise introduced using fundamental commutation relations. By acting on off-shell states and explicitly evaluating trace auxiliary space compute eigenvalues terms roots show that unwanted vanish if equati...

A new type of quantum transfer matrix, arising as a Cholesky factor for the steady-state density matrix of a dissipative Markovian process associated with the boundary-driven Lindblad equation for the isotropic spin-1/2 Heisenberg (XXX ) chain, is presented. The transfer matrix forms a commuting family of non-Hermitian operators depending on the spectral parameter, which is essentially the stre...

The quasi-particle structure of the higher spin XXZ model is studied. We obtained a new description of crystals associated with the level k integrable highest weight Uq(ŝl2) modules in terms of the creation operators at q = 0 (the crystaline spinon basis). The fermionic character formulas and the Yangian structure of those integrable modules naturally follow from this description. We have also ...

The basics of the thermodynamic Bethe ansatz equation are given. The simplest case is repulsive delta function bosons, the thermodynamic equation contains only one unknown function. We also treat the XXX model with spin 1/2 and the XXZ model and the XYZ model. This method is very useful for the investigation of the low temperature thermodynamics of solvable systems.