1990/02/01 by Xiao-Gang Wen · 11 citations
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Quantum Chromodynamics and Particle Interactions #Quantum many-body systems #Physics #Degenerate energy levels #Topological order #Topological degeneracy #Symmetry protected topological order #Topological entropy in physics #Topological quantum computer #Gauge theory #Ground state #Topology (electrical circuits) #Topological quantum number #Quantum mechanics #Theoretical physics #Quantum #Mathematics
paper · doi:10.1142/s0217979290000139
openalex publication_date 1990/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25
We study a new kind of ordering — topological order — in rigid states (the states with no local gapless excitations). We concentrate on characterization of the different topological orders. As an example we discuss in detail chiral spin states of 2 + 1 dimensional spin systems. Chiral spin states are described by the topological Chern-Simons theories in the continuum limit. We show that the topological orders can be characterized by a non-Abelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the non-Abelian gauge structure determines possible fractional statistics of the quasi-particle excitations over the topologically ordered ground states. The dynamics of the low lying global excitations is shown to be independent of random spatial dependent perturbations. The ground state degeneracy and the non-Abelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. We also discuss the symmetry properties of the degenerate ground states of chiral spin states. We find that some degenerate ground states of chiral spin states on torus carry non-trivial quantum numbers of the 90° rotation.