Topological quantum phase transition in the transverse Wen-plaquette model

¹  Department of Physics, Beijing Normal University - Beijing 100875, China
²  Department of Physics, Massachusetts Institute of Technology - Cambridge, MA 02139, USA

Corresponding author: spkou@bnu.edu.cn

Received: 10 June 2008
Accepted: 25 August 2008

Abstract

In this paper we study the quantum phase transition between a quantum state with topological order and that without topological order (TQPT) in the transverse Wen-plaquette model. By mapping the transverse Wen-plaquette model onto the Ising model in a transverse field, some exact results of the TQPT are obtained. The transverse Wen-plaquette model undergoes a continuous TQPT which is characterized in terms of the expectation values of string operators. In particular, the duality relationship between open-string and closed-string is explored —the expectation value of closed-string operator and that of open-string operator play the role of “order parameter” and “disorder order parameter” of the topological order, respectively. At the critical point the “condensation” of both Z₂ vortex and Z₂ charge indicates that the TQPT is a new type of phase transition beyond the Landau-Ginzburg-Wilson paradigm.