Zhao-Xian Yu

Momentum space Z2 number, quantized Berry phase and the quantum phase transitions in spin chain systems

We characterize the quantum phase transitions of gapped time-reversal invariant spin chain systems by nontrivial Z2 numbers derived from a quantized Berry phase in a (1?+?1)-dimensional Bloch momentum space. We study this approach analytically in a general two-band model and give a concrete example in a transverse field XY spin chain system. In our scheme, an extra local gauge transformation is performed to the spin system by a time-dependent twist operator, which endows the Hamiltonian of the system with the topology of a torus without changing its energy spectrum. The Z2 number is obtained by a loop integral of the Berry gauge potential along a quarter of the Brillouin zone. We show that the different phases of the XY spin chain system are distinguished by the Z2 topological order in momentum space.

Berry phase in a quantum system with time-dependent boundary conditions

We discuss the problem of the quantum particle behavior in an infinitely deep elliptical potential well with a moving boundary conditions. We show that this quantum system is equivalent to a particle interacting with a vector field. By introducing the squeezing transformations and making use of the removability of the topological term, the exact Berry phase in a cyclic evolution is calculated.

GEOMETRIC PHASE IN THE CONDENSED VAPOR OF Rb UNDER PRESSURE AND EXTERNAL MAGNETIC FIELD

By using the Lewis–Riesenfeld invariant theory, we have studied the geometric phase in the condensed vapor of Rb under pressure and external time-dependent magnetic field. We find that the geometric phase in the cycle case has nothing to do with the coupling constant between electron and atomic nucleus, and the external time-dependent magnetic field.

GEOMETRIC PHASE IN A GENERALIZED TIME-DEPENDENT GIANT SPIN MODEL

By using of the invariant theory, we have studied the generalized time-dependent giant spin model. The dynamical and geometric phases are given, respectively. The Aharonov–Anandan phase is also obtained under the cyclical evolution.