6 - Correlators, dynamical structure factors and multi-particle excitations

Summary

Introduction

In the previous chapters we showed how series expansion methods can be used to study ground state properties and elementary excitations in simple (and not so simple) antiferromagnets. In the present chapter we extend this to a consideration of more complex properties. We begin by discussing various spin-spin correlation functions, or ‘correlators’. These play an important role in characterizing the nature of the ground state and, as we shall show, can be used to locate quantum phase transition points. The correlators can be combined to form the dynamical twospin structure factors S(k, ω), which are measured in inelastic neutron scattering experiments. We will discuss how these can be computed via series methods, and show some results for the integrated (static) forms.

While one-particle excited states are usually the dominant excitations in quantum systems, there are situations in which two-particle excitations, including bound states, and more general multi-particle excitations also play an important role. There are a number of experimental probes which are beginning to show features associated with multi-particle continuum and bound states, including two-magnon Raman spectroscopy, photo-emission and inelastic neutron scattering. For example, Tennant et al. (2003) have measured two-magnon states in copper nitrate, a quasi one-dimensional antiferromagnet (see Section 6.4.4). Thus one can hope to build up a detailed picture of the dynamics of these quasiparticle excitations, and to construct an effective Hamiltonian to describe them. In the last part of the chapter we outline how one may calculate series expansions for the spectrum of multi-particle excitations in a quantum lattice model at T = 0.