GAUGE FIELDS AND GEOMETRIC PHASES IN PERIODIC SYSTEMS

Abstract

This thesis focuses on gauge fields and geometric phases in periodic systems. The simulation of Aharonov-Bohm effect is discussed in real space with optical lattice. The artificial gauge fields provide convenience in simulating the dynamics of charged particles in magnetic field with neutral atoms. In condensed matter physics, the topological invariants can characterize topological properties of the systems, e.g., Chern number in quantum Hall effect. The geometric phase in one-dimensional optical lattices is employed to study topological phase transitions. In addition, the geometric phase in spin-$1/2$ chains is quite interesting not only in the gapped phase, but also in the regime close to phase transition. We use geometric phases to characterize the critical and noncritical properties in generalized spin-$1/2$ chain with multispin interactions. Moreover, the topological phases are explored via edge states.