Lattice spin models for non-Abelian chiral spin liquids

Lecheminant, P.; Tsvelik, A. M.

doi:10.1103/PhysRevB.95.140406

Title: Lattice spin models for non-Abelian chiral spin liquids

Journal Article · Wed Apr 26 00:00:00 EDT 2017 · Physical Review. B

DOI:https://doi.org/10.1103/PhysRevB.95.140406· OSTI ID:1357956

Lecheminant, P. ^[1]; Tsvelik, A. M. ^[2]

Univ. de Cergy-Pontoise, Cergy-Pontoise Cedex (France)
Brookhaven National Lab. (BNL), Upton, NY (United States)

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.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC00112704; AC02-98CH10886

OSTI ID:: 1357956

Alternate ID(s):: OSTI ID: 1353279

Report Number(s):: BNL-113800-2017-JA; PRBMDO; R&D Project: PO015; KC0202030; TRN: US1702616

Journal Information:: Physical Review. B, Vol. 95, Issue 14; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 24 works

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References (57)

Properties of the chiral spin liquid state in generalized spin ladders Frahm, Holger; Rödenbeck, Claus arXiv https://doi.org/10.48550/arxiv.cond-mat/9702083	text	January 1997
Non-Abelian topological spin liquids from arrays of quantum wires or spin chains Huang, Po-Hao; Chen, Jyong-Hao; Gomes, Pedro R. S. Physical Review B, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevB.93.205123	journal	May 2016
Nature of chiral spin liquids on the kagome lattice Wietek, Alexander; Sterdyniak, Antoine; Läuchli, Andreas M. Physical Review B, Vol. 92, Issue 12 https://doi.org/10.1103/PhysRevB.92.125122	journal	September 2015
Parent Hamiltonian for the non-Abelian chiral spin liquid Greiter, Martin; Schroeter, Darrell F.; Thomale, Ronny Physical Review B, Vol. 89, Issue 16 https://doi.org/10.1103/PhysRevB.89.165125	journal	April 2014
Theory of the spin liquid state of the Heisenberg antiferromagnet Kalmeyer, Vadim; Laughlin, R. B. Physical Review B, Vol. 39, Issue 16 https://doi.org/10.1103/PhysRevB.39.11879	journal	June 1989
Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model Gong, Shou-Shu; Zhu, Wei; Sheng, D. N. Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep06317	journal	September 2014
Ordering in spatially anisotropic triangular antiferromagnets Starykh, Oleg A.; Balents, Leon arXiv https://doi.org/10.48550/arxiv.cond-mat/0607386	text	January 2006
Spatially anisotropic Heisenberg kagome antiferromagnet Apel, W.; Yavors’kii, T.; Everts, H-U Journal of Physics: Condensed Matter, Vol. 19, Issue 14 https://doi.org/10.1088/0953-8984/19/14/145255	journal	March 2007
An exact chiral spin liquid with non-Abelian anyons Yao, Hong; Kivelson, Steven A. arXiv https://doi.org/10.48550/arxiv.0708.0040	text	January 2007
Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level Read, N.; Rezayi, E. Physical Review B, Vol. 59, Issue 12 https://doi.org/10.1103/PhysRevB.59.8084	journal	March 1999
Chiral Spin Liquid in a Frustrated Anisotropic Kagome Heisenberg Model He, Yin-Chen; Sheng, D. N.; Chen, Yan Physical Review Letters, Vol. 112, Issue 13 https://doi.org/10.1103/PhysRevLett.112.137202	journal	April 2014
Equivalence of the resonating-valence-bond and fractional quantum Hall states Kalmeyer, V.; Laughlin, R. B. Physical Review Letters, Vol. 59, Issue 18 https://doi.org/10.1103/PhysRevLett.59.2095	journal	November 1987
Exact Chiral Spin Liquid with Non-Abelian Anyons Yao, Hong; Kivelson, Steven A. Physical Review Letters, Vol. 99, Issue 24 https://doi.org/10.1103/PhysRevLett.99.247203	journal	December 2007
Lattice Laughlin states of bosons and fermions at filling fractions 1/ q Tu, Hong-Hao; Nielsen, Anne E. B.; Cirac, J. Ignacio New Journal of Physics, Vol. 16, Issue 3 https://doi.org/10.1088/1367-2630/16/3/033025	journal	March 2014
Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model He, Yin-Chen; Sheng, D. N.; Chen, Yan arXiv https://doi.org/10.48550/arxiv.1312.3461	text	January 2013
Possible spin-liquid states on the triangular and kagomé lattices Yang, Kun; Warman, L. K.; Girvin, S. M. Physical Review Letters, Vol. 70, Issue 17 https://doi.org/10.1103/PhysRevLett.70.2641	journal	April 1993
Chiral spin liquids in arrays of spin chains Gorohovsky, Gregory; Pereira, Rodrigo G.; Sela, Eran Physical Review B, Vol. 91, Issue 24 https://doi.org/10.1103/PhysRevB.91.245139	journal	June 2015
Ordering in Spatially Anisotropic Triangular Antiferromagnets Starykh, Oleg A.; Balents, Leon Physical Review Letters, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevLett.98.077205	journal	February 2007
Laughlin Spin-Liquid States on Lattices Obtained from Conformal Field Theory Nielsen, Anne E. B.; Cirac, J. Ignacio; Sierra, Germán Physical Review Letters, Vol. 108, Issue 25 https://doi.org/10.1103/PhysRevLett.108.257206	journal	June 2012
Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice Hu, Wen-Jun; Gong, Shou-Shu; Sheng, D. N. Physical Review B, Vol. 94, Issue 7 https://doi.org/10.1103/PhysRevB.94.075131	journal	August 2016
Vacuum degeneracy of chiral spin states in compactified space Wen, X. G. Physical Review B, Vol. 40, Issue 10 https://doi.org/10.1103/PhysRevB.40.7387	journal	October 1989
From Luttinger liquid to non-Abelian quantum Hall states Teo, Jeffrey C. Y.; Kane, C. L. arXiv https://doi.org/10.48550/arxiv.1111.2617	text	January 2011
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator Bauer, B.; Cincio, L.; Keller, B. P. arXiv https://doi.org/10.48550/arxiv.1401.3017	text	January 2014
Spatially anisotropic Heisenberg kagome antiferromagnet Schnyder, Andreas P.; Starykh, Oleg A.; Balents, Leon Physical Review B, Vol. 78, Issue 17 https://doi.org/10.1103/PhysRevB.78.174420	journal	November 2008
Quantum Field Theory in Condensed Matter Physics Tsvelik, Alexi M.; Macdonald, Allan Physics Today, Vol. 50, Issue 2 https://doi.org/10.1063/1.881712	journal	February 1997
Riding a wild horse: Majorana fermions interacting with solitons of fast bosonic fields Tsvelik, A. M. arXiv https://doi.org/10.48550/arxiv.1111.6643	text	January 2011
Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State Schroeter, Darrell F.; Kapit, Eliot; Thomale, Ronny Physical Review Letters, Vol. 99, Issue 9 https://doi.org/10.1103/PhysRevLett.99.097202	journal	August 2007
Local models of fractional quantum Hall states in lattices and physical implementation Nielsen, Anne E. B.; Sierra, Germán; Cirac, J. Ignacio Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms3864	journal	November 2013
Laughlin spin liquid states on lattices obtained from conformal field theory Nielsen, Anne E. B.; Cirac, J. Ignacio; Sierra, German arXiv https://doi.org/10.48550/arxiv.1201.3096	text	January 2012
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator Bauer, B.; Cincio, L.; Keller, B. P. Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms6137	journal	October 2014
Spatially Anisotropic Heisenberg Kagome Antiferromagnet Schnyder, Andreas P.; Starykh, Oleg A.; Balents, Leon arXiv https://doi.org/10.48550/arxiv.0807.0285	text	January 2008
Gapless boundary excitations in the quantum Hall states and in the chiral spin states Wen, X. G. Physical Review B, Vol. 43, Issue 13 https://doi.org/10.1103/PhysRevB.43.11025	journal	May 1991
Bethe ansatz solvable multi-chain quantum systems Zvyagin, A. A. Journal of Physics A: Mathematical and General, Vol. 34, Issue 41 https://doi.org/10.1088/0305-4470/34/41/201	journal	October 2001
Chiral spin liquid and quantum criticality in extended $S = \frac{1}{2}$ Heisenberg models on the triangular lattice Wietek, Alexander; Läuchli, Andreas M. Physical Review B, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevB.95.035141	journal	January 2017
Exact Results for a 1D Kondo Lattice from Bosonization Zachar, Oron; Kivelson, S. A.; Emery, V. J. Physical Review Letters, Vol. 77, Issue 7 https://doi.org/10.1103/PhysRevLett.77.1342	journal	August 1996
Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level Read, N.; Rezayi, E. arXiv https://doi.org/10.48550/arxiv.cond-mat/9809384	text	January 1998
Non-Abelian Statistics in a Quantum Antiferromagnet Greiter, Martin; Thomale, Ronny Physical Review Letters, Vol. 102, Issue 20 https://doi.org/10.1103/PhysRevLett.102.207203	journal	May 2009
Chiral spin states and superconductivity Wen, X. G.; Wilczek, Frank; Zee, A. Physical Review B, Vol. 39, Issue 16 https://doi.org/10.1103/PhysRevB.39.11413	journal	June 1989
Reflections on the one-dimensional realization of odd-frequency pairing Coleman, P.; Georges, A.; Tsvelik, A. M. Journal of Physics: Condensed Matter, Vol. 9, Issue 2 https://doi.org/10.1088/0953-8984/9/2/002	journal	January 1997
From Luttinger liquid to non-Abelian quantum Hall states Teo, Jeffrey C. Y.; Kane, C. L. Physical Review B, Vol. 89, Issue 8 https://doi.org/10.1103/PhysRevB.89.085101	journal	February 2014
Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice Gong, Shou-Shu; Zhu, Wei; Balents, Leon Physical Review B, Vol. 91, Issue 7 https://doi.org/10.1103/PhysRevB.91.075112	journal	February 2015
Large- U limit of a Hubbard model in a magnetic field: Chiral spin interactions and paramagnetism Sen, Diptiman; Chitra, R. Physical Review B, Vol. 51, Issue 3 https://doi.org/10.1103/PhysRevB.51.1922	journal	January 1995
Singlet quantum Hall effect and Chern-Simons theories Balatsky, Alexander; Fradkin, Eduardo Physical Review B, Vol. 43, Issue 13 https://doi.org/10.1103/PhysRevB.43.10622	journal	May 1991
Spatially anisotropic Heisenberg kagome antiferromagnet Apel, W.; Yavors'kii, T.; Al-Hassanieh, K. A. Journal of Physics: Condensed Matter, Vol. 19, Issue 34 https://doi.org/10.1088/0953-8984/19/34/349001	journal	August 2007
Large-$U$ limit of a Hubbard model in a magnetic field: chiral spin interactions and paramagnetism Sen, Diptiman; Chitra, R. arXiv https://doi.org/10.48550/arxiv.cond-mat/9412017	text	January 1994
Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states Fuji, Yohei; He, Yin-Chen; Bhattacharjee, Subhro Physical Review B, Vol. 93, Issue 19 https://doi.org/10.1103/PhysRevB.93.195143	journal	May 2016
Quantum Field Theory in Condensed Matter Physics Tsvelik, Alexei M. Cambridge University Press https://doi.org/10.1017/CBO9780511615832	book	January 2010
Novel local symmetries and chiral-symmetry-broken phases in S=(1/2 triangular-lattice Heisenberg model Baskaran, G. Physical Review Letters, Vol. 63, Issue 22 https://doi.org/10.1103/PhysRevLett.63.2524	journal	November 1989
Coupled-wire construction of chiral spin liquids Meng, Tobias; Neupert, Titus; Greiter, Martin Physical Review B, Vol. 91, Issue 24 https://doi.org/10.1103/PhysRevB.91.241106	journal	June 2015
Non-Abelian Statistics in a Quantum Antiferromagnet Greiter, Martin; Thomale, Ronny arXiv https://doi.org/10.48550/arxiv.0903.4547	text	January 2009
Incommensurate Spin Correlations in Spin- $1 / 2$ Frustrated Two-Leg Heisenberg Ladders Nersesyan, Alexander A.; Gogolin, Alexander O.; Eßler, Fabian H. L. Physical Review Letters, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevLett.81.910	journal	July 1998
Chiral Spin Liquids in Arrays of Spin Chains Gorohovsky, Gregory; Pereira, Rodrigo G.; Sela, Eran arXiv https://doi.org/10.48550/arxiv.1503.05050	text	January 2015
Riding a wild horse: Majorana fermions interacting with solitons of fast bosonic fields Tsvelik, A. M. EPL (Europhysics Letters), Vol. 97, Issue 1 https://doi.org/10.1209/0295-5075/97/17011	journal	January 2012
Properties of the chiral spin liquid state in generalized spin ladders Frahm, Holger; Rödenbeck, Claus Journal of Physics A: Mathematical and General, Vol. 30, Issue 13 https://doi.org/10.1088/0305-4470/30/13/005	journal	July 1997
Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice Hu, Wen-Jun; Gong, Shou-Shu; Sheng, D. N. arXiv https://doi.org/10.48550/arxiv.1603.03365	text	January 2016
Fractional Quantum Hall Effect in an Array of Quantum Wires Kane, C. L.; Mukhopadhyay, Ranjan; Lubensky, T. C. Physical Review Letters, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRevLett.88.036401	journal	January 2002
Relation between the chiral-spin-liquid state and the chiral SU(2) Wess-Zumino-Witten model Balatsky, A. V. Physical Review B, Vol. 43, Issue 1 https://doi.org/10.1103/PhysRevB.43.1257	journal	January 1991

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