skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Ground-state degeneracy of non-Abelian topological phases from coupled wires

Abstract

We construct a family of two-dimensional non-Abelian topological phases from coupled wires using a non-Abelian bosonization approach. We then demonstrate how to determine the nature of the non-Abelian topological order (in particular, the anyonic excitations and the topological degeneracy on the torus) realized in the resulting gapped phases of matter. This paper focuses on the detailed case study of a coupled-wire realization of the bosonic su(2) 2 Moore-Read state, but the approach we outline here can be extended to general bosonic su(2) k topological phases described by non-Abelian Chern-Simons theories. Lastly, we also discuss possible generalizations of this approach to the construction of three-dimensional non-Abelian topological phases.

Authors:
 [1];  [2];  [3];  [4]
  1. Boston Univ., MA (United States); Univ. of California, Santa Barbara, CA (United States); Univ. of Maryland, College Park, MD (United States)
  2. Univ. of Zurich (Switzerland)
  3. Boston Univ., MA (United States)
  4. Paul Scherrer Inst. (PSI), Villigen (Switzerland)
Publication Date:
Research Org.:
Boston Univ., MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1609750
Alternate Identifier(s):
OSTI ID: 1546305
Grant/Contract Number:  
FG02-06ER46316
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 24; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; materials science; physics; toplogical insulators; topological phases in many body systems; topological phases of matter; quantum wires; bosonization; conformal field theory; non-Abelian models; non-Fermi-liquid theory; T-symmetry

Citation Formats

Iadecola, Thomas, Neupert, Titus, Chamon, Claudio, and Mudry, Christopher. Ground-state degeneracy of non-Abelian topological phases from coupled wires. United States: N. p., 2019. Web. doi:10.1103/physrevb.99.245138.
Iadecola, Thomas, Neupert, Titus, Chamon, Claudio, & Mudry, Christopher. Ground-state degeneracy of non-Abelian topological phases from coupled wires. United States. doi:10.1103/physrevb.99.245138.
Iadecola, Thomas, Neupert, Titus, Chamon, Claudio, and Mudry, Christopher. Thu . "Ground-state degeneracy of non-Abelian topological phases from coupled wires". United States. doi:10.1103/physrevb.99.245138. https://www.osti.gov/servlets/purl/1609750.
@article{osti_1609750,
title = {Ground-state degeneracy of non-Abelian topological phases from coupled wires},
author = {Iadecola, Thomas and Neupert, Titus and Chamon, Claudio and Mudry, Christopher},
abstractNote = {We construct a family of two-dimensional non-Abelian topological phases from coupled wires using a non-Abelian bosonization approach. We then demonstrate how to determine the nature of the non-Abelian topological order (in particular, the anyonic excitations and the topological degeneracy on the torus) realized in the resulting gapped phases of matter. This paper focuses on the detailed case study of a coupled-wire realization of the bosonic su(2)2 Moore-Read state, but the approach we outline here can be extended to general bosonic su(2)k topological phases described by non-Abelian Chern-Simons theories. Lastly, we also discuss possible generalizations of this approach to the construction of three-dimensional non-Abelian topological phases.},
doi = {10.1103/physrevb.99.245138},
journal = {Physical Review B},
issn = {2469-9950},
number = 24,
volume = 99,
place = {United States},
year = {2019},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Quantized Hall effect in the field-induced density-wave phases of low-dimensionality conductors
journal, January 1987


Hamiltonian models for topological phases of matter in three spatial dimensions
journal, February 2017


A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations
journal, December 2015


Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
journal, May 2016


Toward classification of conformal theories
journal, May 1988


Integrable Model with Parafermion Zero Energy Modes
journal, August 2014


Coupled wire model of Z 4 orbifold quantum Hall states
journal, August 2018


A current algebra approach to the Kondo effect
journal, June 1990


Braid Statistics in Local Quantum Theory
journal, January 1990


Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection
journal, January 2005


Fractionalization, Topological Order, and Quasiparticle Statistics
journal, February 2006


Correlated topological insulators and the fractional magnetoelectric effect
journal, May 2011


Experimental Realization of a Three-Dimensional Topological Insulator, Bi2Te3
journal, June 2009


Fractional topological phases in three-dimensional coupled-wire systems
journal, September 2015


Chiral spin liquids in arrays of spin chains
journal, June 2015


Discrete spin structures and commuting projector models for two-dimensional fermionic symmetry-protected topological phases
journal, September 2016


Vacuum degeneracy of chiral spin states in compactified space
journal, October 1989


Weyl semimetal from the honeycomb array of topological insulator nanowires
journal, June 2013


A Field Theory of Currents
journal, June 1968


A topological Dirac insulator in a quantum spin Hall phase
journal, April 2008

  • Hsieh, D.; Qian, D.; Wray, L.
  • Nature, Vol. 452, Issue 7190, p. 970-974
  • DOI: 10.1038/nature06843

Current algebra and Wess-Zumino model in two dimensions
journal, December 1984


Local stabilizer codes in three dimensions without string logical operators
journal, April 2011


Cage-Net Fracton Models
journal, April 2019


Local Commuting Projector Hamiltonians and the Quantum Hall Effect
journal, May 2019


Critical theory of overscreened Kondo fixed points
journal, August 1991


(3+1)-TQFTs and topological insulators
journal, July 2011


Coupled spin- 1 2 ladders as microscopic models for non-Abelian chiral spin liquids
journal, April 2017


Two-Dimensional Anisotropic Non-Fermi-Liquid Phase of Coupled Luttinger Liquids
journal, January 2001


Non-Abelian Fractional Quantum hall States and Chiral Coset Conformal Field Theories
journal, December 2000

  • Cabra, D. C.; Fradkin, E.; Rossini, G. L.
  • International Journal of Modern Physics A, Vol. 15, Issue 30
  • DOI: 10.1142/S0217751X00002354

Topological order in an exactly solvable 3D spin model
journal, April 2011


Fermionic symmetry protected topological phases and cobordisms
journal, December 2015

  • Kapustin, Anton; Thorngren, Ryan; Turzillo, Alex
  • Journal of High Energy Physics, Vol. 2015, Issue 12
  • DOI: 10.1007/JHEP12(2015)052

Crossed sliding Luttinger liquid phase
journal, February 2001


Exotic topological order in fractal spin liquids
journal, September 2013


Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
journal, March 2014


A tunable topological insulator in the spin helical Dirac transport regime
journal, July 2009


Model of chiral spin liquids with Abelian and non-Abelian topological phases
journal, December 2017


Topological gauge theories and group cohomology
journal, April 1990

  • Dijkgraaf, Robbert; Witten, Edward
  • Communications in Mathematical Physics, Vol. 129, Issue 2
  • DOI: 10.1007/BF02096988

Consequences of anomalous ward identities
journal, November 1971


Fusion rules and modular transformations in 2D conformal field theory
journal, January 1988


Chiral correlators of the Ising conformal field theory
journal, November 2010


Classification of symmetry-protected phases for interacting fermions in two dimensions
journal, May 2018


Twisted gauge theories in three-dimensional Walker-Wang models
journal, March 2017


Wire constructions of Abelian topological phases in three or more dimensions
journal, May 2016


Fractional Topological Insulators in Three Dimensions
journal, December 2010


Twisted gauge theory model of topological phases in three dimensions
journal, July 2015


Gauging Spatial Symmetries and the Classification of Topological Crystalline Phases
journal, March 2018


Topological quantum glassiness
journal, January 2012


Sliding phases via magnetic fields
journal, January 2001


Network models of quantum percolation and their field-theory representations
journal, October 1994


From Luttinger liquid to non-Abelian quantum Hall states
journal, February 2014


Twisted fracton models in three dimensions
journal, April 2019


The order/disorder quantum field operators associated with the two-dimensional Ising model in the continuum limit
journal, November 1978


Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi 2 Te 3 and Sb 2 Te 3
journal, September 2009


From an array of quantum wires to three-dimensional fractional topological insulators
journal, November 2015


Field-theory treatment of the Heisenberg spin-1 chain
journal, December 1990


Spin TQFTs and fermionic phases of matter
journal, October 2016

  • Gaiotto, Davide; Kapustin, Anton
  • International Journal of Modern Physics A, Vol. 31, Issue 28n29
  • DOI: 10.1142/S0217751X16450445

Quantum Theory of the Smectic Metal State in Stripe Phases
journal, September 2000


Quantum Hall effect in quasi-one-dimensional conductors
journal, May 1991


Topological Insulators in Three Dimensions
journal, March 2007


Edge states and tunneling of non-Abelian quasiparticles in the ν = 5 2 quantum Hall state and p + i p superconductors
journal, January 2007


Classical and quantum conformal field theory
journal, June 1989

  • Moore, Gregory; Seiberg, Nathan
  • Communications in Mathematical Physics, Vol. 123, Issue 2
  • DOI: 10.1007/BF01238857

Coupled-wire construction of chiral spin liquids
journal, June 2015


Topological degeneracy of non-Abelian states for dummies
journal, June 2007


The operator algebra of orbifold models
journal, September 1989

  • Dijkgraaf, Robbert; Vafa, Cumrun; Verlinde, Erik
  • Communications in Mathematical Physics, Vol. 123, Issue 3
  • DOI: 10.1007/BF01238812

The Kondo effect, conformal field theory and fusion rules
journal, April 1991


Theory of twist liquids: Gauging an anyonic symmetry
journal, September 2015


Fault-tolerant quantum computation by anyons
journal, January 2003


Condensate-induced transitions between topologically ordered phases
journal, January 2009


Taming the conformal zoo
journal, April 1989


Topological invariants of time-reversal-invariant band structures
journal, March 2007


Fractional Quantum Hall Effect in an Array of Quantum Wires
journal, January 2002


Cheshire charge in (3+1)-dimensional topological phases
journal, July 2017


Layer Construction of 3D Topological States and String Braiding Statistics
journal, December 2014


The analytic geometry of two-dimensional conformal field theory
journal, February 1987


Wire deconstructionism of two-dimensional topological phases
journal, November 2014


Non-abelian bosonization in two dimensions
journal, December 1984

  • Witten, Edward
  • Communications in Mathematical Physics, Vol. 92, Issue 4
  • DOI: 10.1007/BF01215276

On Classification of Modular Tensor Categories
journal, August 2009

  • Rowell, Eric; Stong, Richard; Wang, Zhenghan
  • Communications in Mathematical Physics, Vol. 292, Issue 2
  • DOI: 10.1007/s00220-009-0908-z

Quantum field theory and the Jones polynomial
journal, September 1989

  • Witten, Edward
  • Communications in Mathematical Physics, Vol. 121, Issue 3
  • DOI: 10.1007/BF01217730

Ising anyons in frustration-free Majorana-dimer models
journal, September 2016


Boson condensation in topologically ordered quantum liquids
journal, March 2016


Curiosities at c = 1
journal, February 1988