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

被引:64
作者
Fendley, P [1 ]
Fradkin, E
机构
[1] Univ Virginia, Dept Phys, Charlottesville, VA 22904 USA
[2] Univ Illinois, Dept Phys, Urbana, IL 61801 USA
基金
美国国家科学基金会;
关键词
D O I
10.1103/PhysRevB.72.024412
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We construct a series of (2+1)-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport of quasiparticles is described by using a correspondence between the braid matrix of the particles and the scattering matrix of (1+1)-dimensional field theories. We discuss in depth lattice and continuum models whose braiding is that of SO(3) Chern-Simons gauge theory, including the simplest type of non-Abelian statistics, involving just one type of quasiparticle. The ground-state wave function of an SO(3) model is related to a loop description of the classical two-dimensional Potts model. We discuss the transition from a topological phase to a conventionally ordered phase, showing in some cases there is a quantum critical point.
引用
收藏
页数:19
相关论文
共 89 条
[1]   QUANTUM-FIELD THEORY OF NON-ABELIAN STRINGS AND VORTICES [J].
ALFORD, MG ;
LEE, KM ;
MARCHRUSSELL, J ;
PRESKILL, J .
NUCLEAR PHYSICS B, 1992, 384 (1-2) :251-317
[2]   THE RESONATING VALENCE BOND STATE IN LA2CUO4 AND SUPERCONDUCTIVITY [J].
ANDERSON, PW .
SCIENCE, 1987, 235 (4793) :1196-1198
[3]   8-VERTEX SOS MODEL AND GENERALIZED ROGERS-RAMANUJAN-TYPE IDENTITIES [J].
ANDREWS, GE ;
BAXTER, RJ ;
FORRESTER, PJ .
JOURNAL OF STATISTICAL PHYSICS, 1984, 35 (3-4) :193-266
[4]   Topological order and conformal quantum critical points [J].
Ardonne, E ;
Fendley, P ;
Fradkin, E .
ANNALS OF PHYSICS, 2004, 310 (02) :493-551
[5]   New class of non-Abelian spin-singlet quantum Hall states [J].
Ardonne, E ;
Schoutens, K .
PHYSICAL REVIEW LETTERS, 1999, 82 (25) :5096-5099
[6]   FRACTIONAL STATISTICS AND THE QUANTUM HALL-EFFECT [J].
AROVAS, D ;
SCHRIEFFER, JR ;
WILCZEK, F .
PHYSICAL REVIEW LETTERS, 1984, 53 (07) :722-723
[7]  
AROVAS D, 1991, 7 INT C REC PROGR MA
[8]  
BAIS FA, 1993, NUCL PHYS B, V393, P547, DOI 10.1016/0550-3213(93)90073-X
[9]   QUANTUM SYMMETRIES IN DISCRETE GAUGE-THEORIES [J].
BAIS, FA ;
VANDRIEL, P ;
PROPITIUS, MD .
PHYSICS LETTERS B, 1992, 280 (1-2) :63-70
[10]   FLUX METAMORPHOSIS [J].
BAIS, FA .
NUCLEAR PHYSICS B, 1980, 170 (01) :32-43