In this paper, we develop an effective mutual Chern-Simons Landau-Ginzburg (MCSLG) theory to describe the continuous topological quantum phase transition (TQPT). In particular, we consider the TQPT between a spin-polarized phase (a state without topological order) and a Z[subscript 2] topologically ordered state. The TQPT is not induced by spontaneous symmetry breaking. Instead the [subscript 2]topological order is broken down by the condensation of [subscript 2] charged quasiparticles. By generalizing the hierarchy theory of fractional quantum Hall effect to [subscript 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.In this paper, we develop an effective mutual Chern-Simons Landau-Ginzburg (MCSLG) theory to describe the continuous topological quantum phase transition (TQPT). In particular, we consider the TQPT between a spin-polarized phase (a state without topological order) and a Z[subscript 2] topologically ordered state. The TQPT is not induced by spontaneous symmetry breaking. Instead the [subscript 2]topological order is broken down by the condensation of [subscript 2] charged quasiparticles. By generalizing the hierarchy theory of fractional quantum Hall effect to [subscript 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.

APSSep 1, 20091 citation

Mutual Chern-Simons Landau-Ginzburg theory for continuous quantum phase transition of Z2 topological order

Su-Peng Kou, Jing Yu, Xiao-Gang Wen

In this paper, we develop an effective mutual Chern-Simons Landau-Ginzburg (MCSLG) theory to describe the continuous topological quantum phase transition (TQPT). In particular, we consider the TQPT between a spin-polarized phase (a state without topological order) and a ${Z}_{2}$ topologically ordered state. The TQPT is not induced by spontaneous symmetry 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.In this paper, we develop an effective mutual Chern-Simons Landau-Ginzburg (MCSLG) theory to describe the continuous topological quantum phase transition (TQPT). In particular, we consider the TQPT between a spin-polarized phase (a state without topological order) and a ${Z}_{2}$ topologically ordered state. The TQPT is not induced by spontaneous symmetry 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.

Physical Review BSep 3, 200916 citations

Landau's theory of phase transitions

Michael El-Batanouny, F. Wooten

Cambridge University Press eBooksMar 13, 20080 citations

Investigation of the Potts Model Using Renormalization-Group Techniques

Geoffrey R. Golner

We report the numerical study, using Wilson's $\ensuremath{\eta}=0$ approximate renormalization-group recursion formula, of a continuous-spin generalization of the three-component Potts model. Previous numerical studies, based on series expansions of the partition function, have indicated strongly that the model has a phase transition of second order. This is in conflict with Landau theory which predicts that the transition be of first order. We find, in agreement with Landau theory, that our model exhibits a first-order phase transition having finite zero-field spontaneous magnetization at the transition point.We report the numerical study, using Wilson's $\ensuremath{\eta}=0$ approximate renormalization-group recursion formula, of a continuous-spin generalization of the three-component Potts model. Previous numerical studies, based on series expansions of the partition function, have indicated strongly that the model has a phase transition of second order. This is in conflict with Landau theory which predicts that the transition be of first order. We find, in agreement with Landau theory, that our model exhibits a first-order phase transition having finite zero-field spontaneous magnetization at the transition point.

Physical review. B, Solid stateOct 1, 1973112 citations

Field theory description of continuous phase transitions

Daniel J. Amit, Marco Zannetti

Journal of Statistical PhysicsJan 1, 197317 citations

{Z}_{2}

topologically ordered state. The TQPT is not induced by spontaneous symmetry 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.