Mutual Chern-Simons Landau-Ginzburg theory for continuous quantum phase transition ofZ2topological order

Su-Peng Kou, Jing Yu, Xiao-Gang Wen
2009 Physical Review B  
Landau-Ginzburg theory for continuous quantum phase transition of Z2 topological order." Physical Review B 80.12 (2009): 125101. In this paper, we develop an effective mutual Chern-Simons Landau-Ginzburg ͑MCSLG͒ theory to describe the continuous topological quantum phase transition ͑TQPT͒. In particular, we consider the TQPT between a spin-polarized phase ͑a state without topological order͒ and a Z 2 topologically ordered state. The TQPT is not induced by spontaneous symmetry breaking. Instead
more » ... breaking. Instead the Z 2 topological order is broken down by the condensation of Z 2 charged quasiparticles. By generalizing the hierarchy theory of fractional quantum Hall effect to Z 2 topological order, we show that the TQPT belongs to the universal class of three-dimensional Ising phase transition. In the end, we applied the MCSLG theory to the toric code model.
doi:10.1103/physrevb.80.125101 fatcat:jverzfn5zvespkfjvqbacltdwq