Integrable Heisenberg-van Vleck chains with variable range exchange

Abstract

The review of recent results in the s=1/2 quantum spin chains with $1/\sinh^2(κr$ exchange is presented. Related problems in the theory of classical and quantum Calogero-Sutherland-Moser systems with inverse square hyperbolic and elliptic potentials are discussed. The attention is paid to finding the explicit form of corresponding Bethe-Ansatz equations and to connection with generalized Hubbard chains in one dimension.