Quasispin Models

Abstract

In elementary quantum mechanics, the spin-$\frac{1}{2}$ system is often taken as the simplest, still non-trivial, example of a two-state system. It allows to point out major quantum properties in the purely abstract space of spin degrees of freedom. Assemblies of spins provide simple models for interacting systems. They are a key model system in solid-state theory, e.g., for spin glasses or strongly interacting electrons (Hubbard model). Here we want to exploit the simplicity provided by a two-level system to understand how elaborate techniques of the many-fermion problem perform in practice. The advantage of such model systems, even if not fully realistic, lies in the fact that most calculations can be performed analytically thanks to straightforward algebraic techniques of angular-momentum algebra. We shall thus use such methods here, in particular to analyze mean-field approaches in some detail.