Realizing non-Abelian statistics in time-reversal-invariant systems

摘要: We construct a series of $(2+1)$-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport is described by using correspondence between the braid matrix particles and scattering $(1+1)$-dimensional field theories. discuss in depth lattice continuum braiding that SO(3) Chern-Simons gauge theory, including simplest type statistics, involving just one quasiparticle. ground-state wave function an model related to loop description classical two-dimensional Potts model. transition from topological phase conventionally ordered phase, showing some cases there quantum critical point.