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Title: 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 Chern-Simons theories in the continuum limit. The authors 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. 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 non-trivial quantum numbers of the 90{degrees} rotation.

Authors:
 [1]
  1. 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 0217-9792
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; THREE-DIMENSIONAL CALCULATIONS; TOPOLOGY; ENERGY LEVELS; ENERGY-LEVEL 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 Chern-Simons theories in the continuum limit. The authors 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. 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 non-trivial 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 = {0217-9792},
number = ,
volume = 4:2,
place = {United States},
year = {1990},
month = {2}
}