Quantum Spin Lattice Models: A Coupled-Cluster Treatment

Abstract

Infinite one-dimensional chains of quantum-mechanical spins interacting via localized (typically nearest-neighbour) interactions, and their obvious extensions to regular lattices in higher numbers of dimensions, have been objects of theoretical interest for a very long time. Indeed, the exact energy eigenstates of the one-dimensional spin-half chain interacting via the isotropic Heisenberg interaction between neighbouring sites,. were exactly solved in principle by Bethe¹ some sixty years ago. Since then the Bethe-ansatz type of solution has been discovered to be applicable to, and fundamental to, a much wider class of integrable Hamiltonian models. This latter feature undoubtedly explains by itself much of the continuing interest in these spin lattice models. Another reason is that, intriguingly, the exact method of Bethe seems to be surprisingly impervious to being extended to deal with similar models in a higher number of dimensions.