Quantized Berry phase in twisted Bloch momentum space as a topological order parameter for spin chains
Abstract
We show that a quantized Berry phase in Bloch momentum space can serve as a topological order parameter to the quantum phases of a gapped spin chain system with timereversal invariance. Specifically, we study this approach analytically in a class of XY spin1/2 chain with multiple sites interactions in a transverse field. In order to derive a proper definition of the Berry curvature in a twodimensional parameter space, we performed a local gauge transformation to the spin chain system by a twist operator, which endows the Hamiltonian of the system with the topology of a torus T^{2} without changing its energy spectrum. We show that a topological Z_{2} order parameter can be obtained as a quantized Berry phase by a loop integral of the Berry gauge potential along quarter of the Brillouin zone, which determines the zerotemperature phase diagram of the system.
 Publication:

Physics Letters A
 Pub Date:
 August 2013
 DOI:
 10.1016/j.physleta.2013.03.021
 Bibcode:
 2013PhLA..377.1250M