Topology Changes and Quantum Phase Transition in SpinChain System
Abstract
The standard LandauGinzburg scenario of phase transition is broken down for quantum phase transition. It is difficult to find an order parameter to indicate different phases for quantum fluctuations. Here, we suggest a topological description of the quantum phase transition for the XY model. The ground states are identified as a specialized U(1) principal bundle on the base manifold $S^2$. And then different first Chern numbers of U(1) principal bundle on the base manifold $S^2$ are associated to each phase of quantum fluctuations. The particlehole picture is used to parameterized the ground states of the XY system. We show that a singularity of the Chern number of the ground states occurs simultaneously with a quantum phase transition. The Chern number is a suitable topological order of the quantum phase transition.
 Publication:

arXiv eprints
 Pub Date:
 January 2008
 DOI:
 10.48550/arXiv.0801.1400
 arXiv:
 arXiv:0801.1400
 Bibcode:
 2008arXiv0801.1400C
 Keywords:

 Quantum Physics
 EPrint:
 5 pages