Geometric Phase in Condensed Matter III: Many-Body Systems

Abstract

In previous chapters, we have considered condensed matter systems that can be described effectively as single-particle problems. In this chapter, we will consider condensed matter systems where interactions between particles are very important. This includes fractional quantum Hall systems, magnetic systems, and Jahn-Teller crystals. A recurrent and central topic in the study of such many-body systems is the dynamical properties of quasi-particles and collective modes. We will show how the concept of geometric phase is used in this context. Due to the complexity caused by the presence of many degrees of freedom, an exact solution of the Schrodinger equation is usually impossible. Nevertheless, there are certain general arguments based on the concept of the geometric phase that allow for useful and sometimes exact results.