Quantum Spin Systems

Abstract

Basically a quantum spin system consists of a set of particles confined to a lattice and interacting at a distance. There are, however, two possible physical interpretations of these models, either as a lattice gas or as a spin system. The first views each point of the lattice as a possible site for a finite number N of particles, i.e., each point of the configuration space can be either empty or occupied by 1, 2,..., N particles. These particles then interact with one another and this leads to an evolution in which one envisages the particles jumping from lattice site to lattice site. The second interpretation assumes that every lattice site is permanently occupied by a particle but the particles have various internal degrees of freedom, e.g., the particles could have an intrinsic spin with several possible orientations. The interaction between the particles then follows from a coupling of the internal degrees of freedom and this yields, for example, an evolution in which the spin orientations are constantly changing.