Topology Changes and Quantum Phase Transition in Spin-Chain System

Details Topology Changes and Quantum Phase Transition in Spin-Chain System Topology Changes and Quantum Phase Transition in Spin-Chain System

2008-01-09

arxiv.org/abs/0801.1400v1

Physics

Quantum Physics

5 pages

Scientific paper

The standard Landau-Ginzburg 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 particle-hole 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.

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