Quantum spin liquid with seven elementary particles

Wang, Haoyu; Changlani, Hitesh J.; Wan, Yuan; Tchernyshyov, Oleg

doi:10.1103/physrevb.95.144425

Title: Quantum spin liquid with seven elementary particles

Abstract

We present an exactly solvable model of a quantum spin liquid with Abelian anyons in d = 2 spatial dimensions. With spins 1/2 on a triangular lattice and six-body interactions, our model has zero spin correlation length and localized elementary excitations like the toric codes of Kitaev and Wen. In contrast to those earlier models, it has more elementary particles—four bosons and three fermions—and higher topological degeneracy of 64 on a torus. Elementary excitations are boson-fermion pairs that come in 12 distinct flavors. We use string operators to expose the topological nature of the model.

Authors:

Wang, Haoyu ^[1]; Changlani, Hitesh J. ^[1]; Wan, Yuan ^[2]; Tchernyshyov, Oleg ^[1]

Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)

Publication Date:: Tue Apr 18 00:00:00 EDT 2017

Research Org.:: Johns Hopkins Univ., Baltimore, MD (United States)

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

OSTI Identifier:: 1535891

Alternate Identifier(s):: OSTI ID: 1352106

Grant/Contract Number:: FG02-08ER46544

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; quantum spin liquid; frustrated magnetism

Citation Formats


                    Wang, Haoyu, Changlani, Hitesh J., Wan, Yuan, and Tchernyshyov, Oleg. Quantum spin liquid with seven elementary particles.  United States: N. p., 2017. 
Web.  doi:10.1103/physrevb.95.144425.

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                    Wang, Haoyu, Changlani, Hitesh J., Wan, Yuan, & Tchernyshyov, Oleg. Quantum spin liquid with seven elementary particles.  United States.  https://doi.org/10.1103/physrevb.95.144425

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                    Wang, Haoyu, Changlani, Hitesh J., Wan, Yuan, and Tchernyshyov, Oleg. Tue .  
"Quantum spin liquid with seven elementary particles".  United States.  https://doi.org/10.1103/physrevb.95.144425.  https://www.osti.gov/servlets/purl/1535891.

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@article{osti_1535891,

  title        = {Quantum spin liquid with seven elementary particles},

  author       = {Wang, Haoyu and Changlani, Hitesh J. and Wan, Yuan and Tchernyshyov, Oleg},

  abstractNote = {We present an exactly solvable model of a quantum spin liquid with Abelian anyons in d = 2 spatial dimensions. With spins 1/2 on a triangular lattice and six-body interactions, our model has zero spin correlation length and localized elementary excitations like the toric codes of Kitaev and Wen. In contrast to those earlier models, it has more elementary particles—four bosons and three fermions—and higher topological degeneracy of 64 on a torus. Elementary excitations are boson-fermion pairs that come in 12 distinct flavors. We use string operators to expose the topological nature of the model.},

  doi          = {10.1103/physrevb.95.144425},

  journal      = {Physical Review B},

  number       = 14,

  volume       = 95,

  place        = {United States},

  year         = {Tue Apr 18 00:00:00 EDT 2017},

  month        = {Tue Apr 18 00:00:00 EDT 2017}

}

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Works referenced in this record:

What is the spin of a spin wave?
journal, October 1981

Faddeev, L. D.; Takhtajan, L. A.
Physics Letters A, Vol. 85, Issue 6-7
DOI: 10.1016/0375-9601(81)90335-2

Rigorous results on valence-bond ground states in antiferromagnets
journal, August 1987

Affleck, Ian; Kennedy, Tom; Lieb, Elliott H.
Physical Review Letters, Vol. 59, Issue 7
DOI: 10.1103/PhysRevLett.59.799

Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
journal, October 2014

Petrova, Olga; Mellado, Paula; Tchernyshyov, Oleg
Physical Review B, Vol. 90, Issue 13
DOI: 10.1103/PhysRevB.90.134404

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet
journal, April 2016

Banerjee, A.; Bridges, C. A.; Yan, J. -Q.
Nature Materials, Vol. 15, Issue 7
DOI: 10.1038/nmat4604

Anyons in an exactly solved model and beyond
journal, January 2006

Kitaev, Alexei
Annals of Physics, Vol. 321, Issue 1
DOI: 10.1016/j.aop.2005.10.005

Quantum order from string-net condensations and the origin of light and massless fermions
journal, September 2003

Wen, Xiao-Gang
Physical Review D, Vol. 68, Issue 6
DOI: 10.1103/PhysRevD.68.065003

Resonating valence bonds: A new kind of insulator?
journal, February 1973

Anderson, P. W.
Materials Research Bulletin, Vol. 8, Issue 2
DOI: 10.1016/0025-5408(73)90167-0

Fault-tolerant quantum computation by anyons
journal, January 2003

Kitaev, A. Yu.
Annals of Physics, Vol. 303, Issue 1
DOI: 10.1016/S0003-4916(02)00018-0

Classifying fractionalization: Symmetry classification of gapped $Z_{2}$ spin liquids in two dimensions
journal, March 2013

Essin, Andrew M.; Hermele, Michael
Physical Review B, Vol. 87, Issue 10
DOI: 10.1103/PhysRevB.87.104406

Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
journal, March 1931

Bethe, H.
Zeitschrift f�r Physik, Vol. 71, Issue 3-4
DOI: 10.1007/BF01341708

Quantum spin liquids: a review
journal, November 2016

Savary, Lucile; Balents, Leon
Reports on Progress in Physics, Vol. 80, Issue 1
DOI: 10.1088/0034-4885/80/1/016502

Unbound spinons in the S =1/2 antiferromagnetic chain ${KCuF}_{3}$
journal, June 1993

Tennant, D. A.; Perring, T. G.; Cowley, R. A.
Physical Review Letters, Vol. 70, Issue 25
DOI: 10.1103/PhysRevLett.70.4003

Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets
journal, April 1989

Read, N.; Sachdev, Subir
Physical Review Letters, Vol. 62, Issue 14
DOI: 10.1103/PhysRevLett.62.1694

Mean-field theory of spin-liquid states with finite energy gap and topological orders
journal, August 1991

Wen, X. G.
Physical Review B, Vol. 44, Issue 6
DOI: 10.1103/PhysRevB.44.2664

Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
journal, June 2013

Mourigal, Martin; Enderle, Mechthild; Klöpperpieper, Axel
Nature Physics, Vol. 9, Issue 7
DOI: 10.1038/nphys2652

Large- n limit of the Heisenberg-Hubbard model: Implications for high- $T_{c}$ superconductors
journal, March 1988

Affleck, Ian; Marston, J. Brad
Physical Review B, Vol. 37, Issue 7
DOI: 10.1103/PhysRevB.37.3774

Majorana edge states for $Z_{2}$ topological orders of the Wen plaquette and toric code models
journal, May 2013

Yu, Jing; Zhang, Xing-Hai; Kou, Su-Peng
Physical Review B, Vol. 87, Issue 18
DOI: 10.1103/PhysRevB.87.184402

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
journal, January 2009

Jackeli, G.; Khaliullin, G.
Physical Review Letters, Vol. 102, Issue 1
DOI: 10.1103/PhysRevLett.102.017205

Quantum Orders in an Exact Soluble Model
journal, January 2003

Wen, Xiao-Gang
Physical Review Letters, Vol. 90, Issue 1
DOI: 10.1103/PhysRevLett.90.016803

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Title: Quantum spin liquid with seven elementary particles

Abstract

Citation Formats

What is the spin of a spin wave? journal, October 1981

Rigorous results on valence-bond ground states in antiferromagnets journal, August 1987

Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model journal, October 2014

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet journal, April 2016

Anyons in an exactly solved model and beyond journal, January 2006

Quantum order from string-net condensations and the origin of light and massless fermions journal, September 2003

Resonating valence bonds: A new kind of insulator? journal, February 1973

Fault-tolerant quantum computation by anyons journal, January 2003

Classifying fractionalization: Symmetry classification of gapped Z 2 spin liquids in two dimensions journal, March 2013

Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette journal, March 1931

Quantum spin liquids: a review journal, November 2016

Unbound spinons in the S =1/2 antiferromagnetic chain KCuF 3 journal, June 1993

Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets journal, April 1989

Mean-field theory of spin-liquid states with finite energy gap and topological orders journal, August 1991

Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain journal, June 2013

Large- n limit of the Heisenberg-Hubbard model: Implications for high- T c superconductors journal, March 1988

Majorana edge states for Z 2 topological orders of the Wen plaquette and toric code models journal, May 2013

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models journal, January 2009

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What is the spin of a spin wave?
journal, October 1981

Rigorous results on valence-bond ground states in antiferromagnets
journal, August 1987

Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
journal, October 2014

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet
journal, April 2016

Anyons in an exactly solved model and beyond
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Quantum order from string-net condensations and the origin of light and massless fermions
journal, September 2003

Resonating valence bonds: A new kind of insulator?
journal, February 1973

Fault-tolerant quantum computation by anyons
journal, January 2003

Classifying fractionalization: Symmetry classification of gapped $Z_{2}$ spin liquids in two dimensions
journal, March 2013

Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
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Quantum spin liquids: a review
journal, November 2016

Unbound spinons in the S =1/2 antiferromagnetic chain ${KCuF}_{3}$
journal, June 1993

Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets
journal, April 1989

Mean-field theory of spin-liquid states with finite energy gap and topological orders
journal, August 1991

Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
journal, June 2013

Large- n limit of the Heisenberg-Hubbard model: Implications for high- $T_{c}$ superconductors
journal, March 1988

Majorana edge states for $Z_{2}$ topological orders of the Wen plaquette and toric code models
journal, May 2013

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
journal, January 2009

Quantum Orders in an Exact Soluble Model
journal, January 2003