Topological orders in rigid states
Abstract
The authors study a new kind of ordering topological order in rigid states (the states with no local gapless excitations). This paper concentrates on characterization of the different topological orders. As an example the authors discuss in detail chiral spin states of 2+1 dimensional spin systems. Chiral spin states are described by the topological ChernSimons theories in the continuum limit. The authors show that the topological orders can be characterized by a nonAbelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the nonAbelian gauge structure determines possible fractional statistics of the quasiparticle 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 nonAbelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. The authors also discuss the symmetry properties of the degenerate ground states of chiral spin states. The authors find that some degenerate ground states of chiral spin states on torus carry nontrivial quantum numbers of the 90{degrees} rotation.
 Authors:

 School of Natural Sciences, Inst. for Advanced Study, Princeton, NJ (US)
 Publication Date:
 OSTI Identifier:
 5071770
 Resource Type:
 Journal Article
 Journal Name:
 International Journal of Modern Physics B; (United States)
 Additional Journal Information:
 Journal Volume: 4:2; Journal ID: ISSN 02179792
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MAGNETS; GROUND STATES; CHIRALITY; EXCITATION; GAUGE INVARIANCE; HAMILTONIANS; QUASI PARTICLES; THREEDIMENSIONAL CALCULATIONS; TOPOLOGY; ENERGY LEVELS; ENERGYLEVEL TRANSITIONS; INVARIANCE PRINCIPLES; MATHEMATICAL OPERATORS; MATHEMATICS; PARTICLE PROPERTIES; QUANTUM OPERATORS; 656000*  Condensed Matter Physics; 657002  Theoretical & Mathematical Physics Classical & Quantum Mechanics
Citation Formats
Wen, X G. Topological orders in rigid states. United States: N. p., 1990.
Web. doi:10.1142/S0217979290000139.
Wen, X G. Topological orders in rigid states. United States. https://doi.org/10.1142/S0217979290000139
Wen, X G. Thu .
"Topological orders in rigid states". United States. https://doi.org/10.1142/S0217979290000139.
@article{osti_5071770,
title = {Topological orders in rigid states},
author = {Wen, X G},
abstractNote = {The authors study a new kind of ordering topological order in rigid states (the states with no local gapless excitations). This paper concentrates on characterization of the different topological orders. As an example the authors discuss in detail chiral spin states of 2+1 dimensional spin systems. Chiral spin states are described by the topological ChernSimons theories in the continuum limit. The authors show that the topological orders can be characterized by a nonAbelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the nonAbelian gauge structure determines possible fractional statistics of the quasiparticle 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 nonAbelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. The authors also discuss the symmetry properties of the degenerate ground states of chiral spin states. The authors find that some degenerate ground states of chiral spin states on torus carry nontrivial quantum numbers of the 90{degrees} rotation.},
doi = {10.1142/S0217979290000139},
url = {https://www.osti.gov/biblio/5071770},
journal = {International Journal of Modern Physics B; (United States)},
issn = {02179792},
number = ,
volume = 4:2,
place = {United States},
year = {1990},
month = {2}
}