Integrable Heisenberg-van Vleck chains with variable range exchange

TL;DR

This paper reviews recent advances in s=1/2 quantum spin chains with variable-range hyperbolic exchange interactions, connecting them to classical integrable systems and generalized Hubbard models.

Contribution

It provides explicit Bethe-Ansatz equations for these chains and explores their relation to Calogero-Sutherland-Moser systems and Hubbard chains.

Findings

Explicit Bethe-Ansatz equations derived

Connections established with Calogero-Sutherland-Moser systems

Insights into generalized Hubbard chains in 1D

Abstract

The review of recent results in the s=1/2 quantum spin chains with $1/\sinh^2(\kappa r$ 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.