Lattice spin models for non-Abelian chiral spin liquids
Abstract
Here, we suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids—spin analogs of fractional non-Abelian quantum Hall states—with gapped bulk and gapless chiral edge excitations described by the SU(2)n Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-n/2 ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)n gapless edge excitations.
- Authors:
-
- Univ. de Cergy-Pontoise, Cergy-Pontoise Cedex (France)
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1357956
- Alternate Identifier(s):
- OSTI ID: 1353279
- Report Number(s):
- BNL-113800-2017-JA
Journal ID: ISSN 2469-9950; PRBMDO; R&D Project: PO015; KC0202030; TRN: US1702616
- Grant/Contract Number:
- SC00112704; AC02-98CH10886
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 14; 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
Citation Formats
Lecheminant, P., and Tsvelik, A. M. Lattice spin models for non-Abelian chiral spin liquids. United States: N. p., 2017.
Web. doi:10.1103/PhysRevB.95.140406.
Lecheminant, P., & Tsvelik, A. M. Lattice spin models for non-Abelian chiral spin liquids. United States. https://doi.org/10.1103/PhysRevB.95.140406
Lecheminant, P., and Tsvelik, A. M. Wed .
"Lattice spin models for non-Abelian chiral spin liquids". United States. https://doi.org/10.1103/PhysRevB.95.140406. https://www.osti.gov/servlets/purl/1357956.
@article{osti_1357956,
title = {Lattice spin models for non-Abelian chiral spin liquids},
author = {Lecheminant, P. and Tsvelik, A. M.},
abstractNote = {Here, we suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids—spin analogs of fractional non-Abelian quantum Hall states—with gapped bulk and gapless chiral edge excitations described by the SU(2)n Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-n/2 ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)n gapless edge excitations.},
doi = {10.1103/PhysRevB.95.140406},
journal = {Physical Review. B},
number = 14,
volume = 95,
place = {United States},
year = {Wed Apr 26 00:00:00 EDT 2017},
month = {Wed Apr 26 00:00:00 EDT 2017}
}
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Works referenced in this record:
Properties of the chiral spin liquid state in generalized spin ladders
text, January 1997
- Frahm, Holger; Rödenbeck, Claus
- arXiv
Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
journal, May 2016
- Huang, Po-Hao; Chen, Jyong-Hao; Gomes, Pedro R. S.
- Physical Review B, Vol. 93, Issue 20
Nature of chiral spin liquids on the kagome lattice
journal, September 2015
- Wietek, Alexander; Sterdyniak, Antoine; Läuchli, Andreas M.
- Physical Review B, Vol. 92, Issue 12
Parent Hamiltonian for the non-Abelian chiral spin liquid
journal, April 2014
- Greiter, Martin; Schroeter, Darrell F.; Thomale, Ronny
- Physical Review B, Vol. 89, Issue 16
Theory of the spin liquid state of the Heisenberg antiferromagnet
journal, June 1989
- Kalmeyer, Vadim; Laughlin, R. B.
- Physical Review B, Vol. 39, Issue 16
Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
journal, September 2014
- Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.
- Scientific Reports, Vol. 4, Issue 1
Ordering in spatially anisotropic triangular antiferromagnets
text, January 2006
- Starykh, Oleg A.; Balents, Leon
- arXiv
Spatially anisotropic Heisenberg kagome antiferromagnet
journal, March 2007
- Apel, W.; Yavors’kii, T.; Everts, H-U
- Journal of Physics: Condensed Matter, Vol. 19, Issue 14
An exact chiral spin liquid with non-Abelian anyons
text, January 2007
- Yao, Hong; Kivelson, Steven A.
- arXiv
Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level
journal, March 1999
- Read, N.; Rezayi, E.
- Physical Review B, Vol. 59, Issue 12
Chiral Spin Liquid in a Frustrated Anisotropic Kagome Heisenberg Model
journal, April 2014
- He, Yin-Chen; Sheng, D. N.; Chen, Yan
- Physical Review Letters, Vol. 112, Issue 13
Equivalence of the resonating-valence-bond and fractional quantum Hall states
journal, November 1987
- Kalmeyer, V.; Laughlin, R. B.
- Physical Review Letters, Vol. 59, Issue 18
Exact Chiral Spin Liquid with Non-Abelian Anyons
journal, December 2007
- Yao, Hong; Kivelson, Steven A.
- Physical Review Letters, Vol. 99, Issue 24
Lattice Laughlin states of bosons and fermions at filling fractions 1/ q
journal, March 2014
- Tu, Hong-Hao; Nielsen, Anne E. B.; Cirac, J. Ignacio
- New Journal of Physics, Vol. 16, Issue 3
Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
text, January 2013
- He, Yin-Chen; Sheng, D. N.; Chen, Yan
- arXiv
Possible spin-liquid states on the triangular and kagomé lattices
journal, April 1993
- Yang, Kun; Warman, L. K.; Girvin, S. M.
- Physical Review Letters, Vol. 70, Issue 17
Chiral spin liquids in arrays of spin chains
journal, June 2015
- Gorohovsky, Gregory; Pereira, Rodrigo G.; Sela, Eran
- Physical Review B, Vol. 91, Issue 24
Ordering in Spatially Anisotropic Triangular Antiferromagnets
journal, February 2007
- Starykh, Oleg A.; Balents, Leon
- Physical Review Letters, Vol. 98, Issue 7
Laughlin Spin-Liquid States on Lattices Obtained from Conformal Field Theory
journal, June 2012
- Nielsen, Anne E. B.; Cirac, J. Ignacio; Sierra, Germán
- Physical Review Letters, Vol. 108, Issue 25
Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice
journal, August 2016
- Hu, Wen-Jun; Gong, Shou-Shu; Sheng, D. N.
- Physical Review B, Vol. 94, Issue 7
Vacuum degeneracy of chiral spin states in compactified space
journal, October 1989
- Wen, X. G.
- Physical Review B, Vol. 40, Issue 10
From Luttinger liquid to non-Abelian quantum Hall states
text, January 2011
- Teo, Jeffrey C. Y.; Kane, C. L.
- arXiv
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
text, January 2014
- Bauer, B.; Cincio, L.; Keller, B. P.
- arXiv
Spatially anisotropic Heisenberg kagome antiferromagnet
journal, November 2008
- Schnyder, Andreas P.; Starykh, Oleg A.; Balents, Leon
- Physical Review B, Vol. 78, Issue 17
Quantum Field Theory in Condensed Matter Physics
journal, February 1997
- Tsvelik, Alexi M.; Macdonald, Allan
- Physics Today, Vol. 50, Issue 2
Riding a wild horse: Majorana fermions interacting with solitons of fast bosonic fields
text, January 2011
- Tsvelik, A. M.
- arXiv
Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
journal, August 2007
- Schroeter, Darrell F.; Kapit, Eliot; Thomale, Ronny
- Physical Review Letters, Vol. 99, Issue 9
Local models of fractional quantum Hall states in lattices and physical implementation
journal, November 2013
- Nielsen, Anne E. B.; Sierra, Germán; Cirac, J. Ignacio
- Nature Communications, Vol. 4, Issue 1
Laughlin spin liquid states on lattices obtained from conformal field theory
text, January 2012
- Nielsen, Anne E. B.; Cirac, J. Ignacio; Sierra, German
- arXiv
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
journal, October 2014
- Bauer, B.; Cincio, L.; Keller, B. P.
- Nature Communications, Vol. 5, Issue 1
Spatially Anisotropic Heisenberg Kagome Antiferromagnet
text, January 2008
- Schnyder, Andreas P.; Starykh, Oleg A.; Balents, Leon
- arXiv
Gapless boundary excitations in the quantum Hall states and in the chiral spin states
journal, May 1991
- Wen, X. G.
- Physical Review B, Vol. 43, Issue 13
Bethe ansatz solvable multi-chain quantum systems
journal, October 2001
- Zvyagin, A. A.
- Journal of Physics A: Mathematical and General, Vol. 34, Issue 41
Chiral spin liquid and quantum criticality in extended Heisenberg models on the triangular lattice
journal, January 2017
- Wietek, Alexander; Läuchli, Andreas M.
- Physical Review B, Vol. 95, Issue 3
Exact Results for a 1D Kondo Lattice from Bosonization
journal, August 1996
- Zachar, Oron; Kivelson, S. A.; Emery, V. J.
- Physical Review Letters, Vol. 77, Issue 7
Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
text, January 1998
- Read, N.; Rezayi, E.
- arXiv
Non-Abelian Statistics in a Quantum Antiferromagnet
journal, May 2009
- Greiter, Martin; Thomale, Ronny
- Physical Review Letters, Vol. 102, Issue 20
Chiral spin states and superconductivity
journal, June 1989
- Wen, X. G.; Wilczek, Frank; Zee, A.
- Physical Review B, Vol. 39, Issue 16
Reflections on the one-dimensional realization of odd-frequency pairing
journal, January 1997
- Coleman, P.; Georges, A.; Tsvelik, A. M.
- Journal of Physics: Condensed Matter, Vol. 9, Issue 2
From Luttinger liquid to non-Abelian quantum Hall states
journal, February 2014
- Teo, Jeffrey C. Y.; Kane, C. L.
- Physical Review B, Vol. 89, Issue 8
Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice
journal, February 2015
- Gong, Shou-Shu; Zhu, Wei; Balents, Leon
- Physical Review B, Vol. 91, Issue 7
Large- U limit of a Hubbard model in a magnetic field: Chiral spin interactions and paramagnetism
journal, January 1995
- Sen, Diptiman; Chitra, R.
- Physical Review B, Vol. 51, Issue 3
Singlet quantum Hall effect and Chern-Simons theories
journal, May 1991
- Balatsky, Alexander; Fradkin, Eduardo
- Physical Review B, Vol. 43, Issue 13
Spatially anisotropic Heisenberg kagome antiferromagnet
journal, August 2007
- Apel, W.; Yavors'kii, T.; Al-Hassanieh, K. A.
- Journal of Physics: Condensed Matter, Vol. 19, Issue 34
Large-$U$ limit of a Hubbard model in a magnetic field: chiral spin interactions and paramagnetism
text, January 1994
- Sen, Diptiman; Chitra, R.
- arXiv
Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
journal, May 2016
- Fuji, Yohei; He, Yin-Chen; Bhattacharjee, Subhro
- Physical Review B, Vol. 93, Issue 19
Quantum Field Theory in Condensed Matter Physics
book, January 2010
- Tsvelik, Alexei M.
- Cambridge University Press
Novel local symmetries and chiral-symmetry-broken phases in S=(1/2 triangular-lattice Heisenberg model
journal, November 1989
- Baskaran, G.
- Physical Review Letters, Vol. 63, Issue 22
Coupled-wire construction of chiral spin liquids
journal, June 2015
- Meng, Tobias; Neupert, Titus; Greiter, Martin
- Physical Review B, Vol. 91, Issue 24
Non-Abelian Statistics in a Quantum Antiferromagnet
text, January 2009
- Greiter, Martin; Thomale, Ronny
- arXiv
Incommensurate Spin Correlations in Spin- Frustrated Two-Leg Heisenberg Ladders
journal, July 1998
- Nersesyan, Alexander A.; Gogolin, Alexander O.; Eßler, Fabian H. L.
- Physical Review Letters, Vol. 81, Issue 4
Chiral Spin Liquids in Arrays of Spin Chains
text, January 2015
- Gorohovsky, Gregory; Pereira, Rodrigo G.; Sela, Eran
- arXiv
Riding a wild horse: Majorana fermions interacting with solitons of fast bosonic fields
journal, January 2012
- Tsvelik, A. M.
- EPL (Europhysics Letters), Vol. 97, Issue 1
Properties of the chiral spin liquid state in generalized spin ladders
journal, July 1997
- Frahm, Holger; Rödenbeck, Claus
- Journal of Physics A: Mathematical and General, Vol. 30, Issue 13
Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice
text, January 2016
- Hu, Wen-Jun; Gong, Shou-Shu; Sheng, D. N.
- arXiv
Fractional Quantum Hall Effect in an Array of Quantum Wires
journal, January 2002
- Kane, C. L.; Mukhopadhyay, Ranjan; Lubensky, T. C.
- Physical Review Letters, Vol. 88, Issue 3
Relation between the chiral-spin-liquid state and the chiral SU(2) Wess-Zumino-Witten model
journal, January 1991
- Balatsky, A. V.
- Physical Review B, Vol. 43, Issue 1
Works referencing / citing this record:
Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
text, January 2018
- Chen, Ji-Yao; Vanderstraeten, Laurens; Capponi, Sylvain
- arXiv
Non-Abelian chiral spin liquid on a simple non-Archimedean lattice
journal, January 2020
- Peri, V.; Ok, S.; Tsirkin, S. S.
- Physical Review B, Vol. 101, Issue 4
Non-Abelian chiral spin liquid on a simple non-Archimedean lattice
text, January 2019
- Peri, Valerio; Ok, Seulgi; Tsirkin, S. S.
- University of Zurich
Coupled-wire constructions: a Luttinger liquid approach to topology
journal, February 2020
- Meng, Tobias
- The European Physical Journal Special Topics, Vol. 229, Issue 4
Non-Abelian chiral spin liquid on a simple non-Archimedean lattice
text, January 2020
- Peri, V.; Ok, S.; Tsirkin, S. S.
- American Physical Society
Spin Chain Network Construction of Chiral Spin Liquids
journal, September 2019
- Ferraz, Gabriel; Ramos, Flávia B.; Egger, Reinhold
- Physical Review Letters, Vol. 123, Issue 13
Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
journal, November 2018
- Chen, Ji-Yao; Vanderstraeten, Laurens; Capponi, Sylvain
- Physical Review B, Vol. 98, Issue 18
From coupled wires to coupled layers: Model with three-dimensional fractional excitations
journal, June 2019
- Fuji, Yohei; Furusaki, Akira
- Physical Review B, Vol. 99, Issue 24
Spin chain network construction of chiral spin liquids
text, January 2019
- Ferraz, Gabriel; Ramos, Flavia B.; Egger, Reinhold
- arXiv
Model of spin liquids with and without time-reversal symmetry
text, January 2018
- Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio
- arXiv
Exact diagonalization of SU( ) Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains using the full SU( ) symmetry
journal, September 2017
- Wan, Kianna; Nataf, Pierre; Mila, Frédéric
- Physical Review B, Vol. 96, Issue 11
Coupled-wire constructions: a Luttinger liquid approach to topology
text, January 2019
- Meng, Tobias
- arXiv
Gapless chiral spin liquid from coupled chains on the kagome lattice
journal, January 2018
- Pereira, Rodrigo; Bieri, Samuel
- SciPost Physics, Vol. 4, Issue 1
Model of spin liquids with and without time-reversal symmetry
journal, May 2019
- Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio
- Physical Review B, Vol. 99, Issue 18
Density matrix renormalization group simulations of SU( ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz
journal, April 2018
- Nataf, Pierre; Mila, Frédéric
- Physical Review B, Vol. 97, Issue 13