Momentum space Z2 number, quantized Berry phase and the quantum phase transitions in spin chain systems
Department of Physics and Electronic Science, Beijing Information Science and Technology University Beijing 100192, China
Received: 20 August 2012
Accepted: 26 November 2012
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.
PACS: 03.65.Vf – Phases: geometric; dynamic or topological / 75.10.Jm – Quantized spin models, including quantum spin frustration / 73.43.Nq – Quantum phase transitions
© EPLA, 2012