Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model

Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.

doi:10.1038/srep06317

Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model

Journal Article · Wed Sep 10 00:00:00 EDT 2014 · Scientific Reports

DOI:https://doi.org/10.1038/srep06317· OSTI ID:1624741

Gong, Shou-Shu ^[1]; Zhu, Wei ^[2]; Sheng, D. N. ^[2]

California State Univ. (CalState), Northridge, CA (United States). Dept. of Physics and Astronomy; DOE/OSTI
California State Univ. (CalState), Northridge, CA (United States). Dept. of Physics and Astronomy

The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a spin-$$ \frac{1}{2}$$ isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified Z2 spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids.

View Accepted Manuscript (DOE)

Research Organization:: California State Univ. (CalState), Long Beach, CA (United States)

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

Grant/Contract Number:: FG02-06ER46305

OSTI ID:: 1624741

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 4; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

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Lattice spin models for non-Abelian chiral spin liquids Lecheminant, P.; Tsvelik, A. M. Physical Review B, Vol. 95, Issue 14 https://doi.org/10.1103/physrevb.95.140406	journal	April 2017
Gapped spin liquid with Z 2 topological order for the kagome Heisenberg model Mei, Jia-Wei; Chen, Ji-Yao; He, Huan Physical Review B, Vol. 95, Issue 23 https://doi.org/10.1103/physrevb.95.235107	journal	June 2017
Global phase diagram and quantum spin liquids in a spin- 1 2 triangular antiferromagnet Gong, Shou-Shu; Zhu, W.; Zhu, J. -X. Physical Review B, Vol. 96, Issue 7 https://doi.org/10.1103/physrevb.96.075116	journal	August 2017
Chiral liquid phase of simple quantum magnets Wang, Zhentao; Feiguin, Adrian E.; Zhu, Wei Physical Review B, Vol. 96, Issue 18 https://doi.org/10.1103/physrevb.96.184409	journal	November 2017
Measuring space-group symmetry fractionalization in Z 2 spin liquids Zaletel, Michael P.; Lu, Yuan-Ming; Vishwanath, Ashvin Physical Review B, Vol. 96, Issue 19 https://doi.org/10.1103/physrevb.96.195164	journal	November 2017
Critical behavior of the QED 3 -Gross-Neveu model: Duality and deconfined criticality Janssen, Lukas; He, Yin-Chen Physical Review B, Vol. 96, Issue 20 https://doi.org/10.1103/physrevb.96.205113	journal	November 2017
Stability of the spin- 1 2 kagome ground state with breathing anisotropy Repellin, Cécile; He, Yin-Chen; Pollmann, Frank Physical Review B, Vol. 96, Issue 20 https://doi.org/10.1103/physrevb.96.205124	journal	November 2017
Ground-state phase diagram of the triangular lattice Hubbard model by the density-matrix renormalization group method Shirakawa, Tomonori; Tohyama, Takami; Kokalj, Jure Physical Review B, Vol. 96, Issue 20 https://doi.org/10.1103/physrevb.96.205130	journal	November 2017
Degenerate and chiral states in the extended Heisenberg model on the kagome lattice Gómez Albarracín, F. A.; Pujol, P. Physical Review B, Vol. 97, Issue 10 https://doi.org/10.1103/physrevb.97.104419	journal	March 2018
Quantum spin circulator in Y junctions of Heisenberg chains Buccheri, Francesco; Egger, Reinhold; Pereira, Rodrigo G. Physical Review B, Vol. 97, Issue 22 https://doi.org/10.1103/physrevb.97.220402	journal	June 2018
Classical phase diagram of the stuffed honeycomb lattice Sahoo, Jyotisman; Kochkov, Dmitrii; Clark, Bryan K. Physical Review B, Vol. 98, Issue 13 https://doi.org/10.1103/physrevb.98.134419	journal	October 2018
Distinct Spin Liquids and Their Transitions in Spin- 1 / 2 X X Z Kagome Antiferromagnets He, Yin-Chen; Chen, Yan Physical Review Letters, Vol. 114, Issue 3 https://doi.org/10.1103/physrevlett.114.037201	journal	January 2015
Constraints on Topological Order in Mott Insulators Zaletel, Michael P.; Vishwanath, Ashvin Physical Review Letters, Vol. 114, Issue 7 https://doi.org/10.1103/physrevlett.114.077201	journal	February 2015
Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms Glaetzle, Alexander W.; Dalmonte, Marcello; Nath, Rejish Physical Review Letters, Vol. 114, Issue 17 https://doi.org/10.1103/physrevlett.114.173002	journal	April 2015
Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons Nasu, Joji; Motome, Yukitoshi Physical Review Letters, Vol. 115, Issue 8 https://doi.org/10.1103/physrevlett.115.087203	journal	August 2015
Statistical Transmutation in Floquet Driven Optical Lattices Sedrakyan, Tigran A.; Galitski, Victor M.; Kamenev, Alex Physical Review Letters, Vol. 115, Issue 19 https://doi.org/10.1103/physrevlett.115.195301	journal	November 2015
Kagome Chiral Spin Liquid as a Gauged U ( 1 ) Symmetry Protected Topological Phase He, Yin-Chen; Bhattacharjee, Subhro; Pollmann, Frank Physical Review Letters, Vol. 115, Issue 26 https://doi.org/10.1103/physrevlett.115.267209	journal	December 2015
Chiral Spin Liquids in Triangular-Lattice SU ( N ) Fermionic Mott Insulators with Artificial Gauge Fields Nataf, Pierre; Lajkó, Miklós; Wietek, Alexander Physical Review Letters, Vol. 117, Issue 16 https://doi.org/10.1103/physrevlett.117.167202	journal	October 2016
Signatures of Dirac Cones in a DMRG Study of the Kagome Heisenberg Model He, Yin-Chen; Zaletel, Michael P.; Oshikawa, Masaki Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/physrevx.7.031020	journal	July 2017
Neural-Network Quantum States, String-Bond States, and Chiral Topological States Glasser, Ivan; Pancotti, Nicola; August, Moritz Physical Review X, Vol. 8, Issue 1 https://doi.org/10.1103/physrevx.8.011006	journal	January 2018
Emergent Multi-Flavor QED 3 at the Plateau Transition between Fractional Chern Insulators: Applications to Graphene Heterostructures Lee, Jong Yeon; Wang, Chong; Zaletel, Michael P. Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/physrevx.8.031015	journal	July 2018
Quantum spin liquid states Zhou, Yi; Kanoda, Kazushi; Ng, Tai-Kai Reviews of Modern Physics, Vol. 89, Issue 2 https://doi.org/10.1103/revmodphys.89.025003	journal	April 2017
Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices Lima, F. Crasto De; Ferreira, Gerson J.; Miwa, R. H. Unpublished https://doi.org/10.13140/rg.2.2.32912.35849	text	January 2019
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
Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms Glaetzle, Alexander W.; Dalmonte, Marcello; Nath, Rejish arXiv https://doi.org/10.48550/arxiv.1410.3388	text	January 2014
Gapless chiral spin liquid in a kagome Heisenberg model Bieri, Samuel; Messio, Laura; Bernu, Bernard arXiv https://doi.org/10.48550/arxiv.1411.1622	text	January 2014
Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group Zhu, W.; Gong, S. S.; Haldane, F. D. M. arXiv https://doi.org/10.48550/arxiv.1412.8115	text	January 2014
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
Statistical transmutation in Floquet driven optical lattices Sedrakyan, Tigran A.; Galitski, Victor M.; Kamenev, Alex arXiv https://doi.org/10.48550/arxiv.1506.00721	text	January 2015
A Quantum Dipolar Spin Liquid Yao, Norman Y.; Zaletel, Michael P.; Stamper-Kurn, Dan M. arXiv https://doi.org/10.48550/arxiv.1510.06403	text	January 2015
Projective symmetry group classification of chiral spin liquids Bieri, Samuel; Lhuillier, Claire; Messio, Laura arXiv https://doi.org/10.48550/arxiv.1512.00324	text	January 2015
Ground state phase diagram of the triangular lattice Hubbard model by density matrix renormalization group method Shirakawa, Tomonori; Tohyama, Takami; Kokalj, Jure arXiv https://doi.org/10.48550/arxiv.1606.06814	text	January 2016
Spin structure factors of chiral quantum spin liquids on the kagome lattice Halimeh, Jad C.; Punk, Matthias arXiv https://doi.org/10.48550/arxiv.1606.07856	text	January 2016
Quantum Spin Liquid States Zhou, Yi; Kanoda, Kazushi; Ng, Tai-Kai arXiv https://doi.org/10.48550/arxiv.1607.03228	text	January 2016
Lattice effects on Laughlin wave functions and parent Hamiltonians Glasser, Ivan; Cirac, J. Ignacio; Sierra, Germán arXiv https://doi.org/10.48550/arxiv.1609.02435	text	January 2016
Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model He, Yin-Chen; Zaletel, Michael P.; Oshikawa, Masaki arXiv https://doi.org/10.48550/arxiv.1611.06238	text	January 2016
Neural-Network Quantum States, String-Bond States, and Chiral Topological States Glasser, Ivan; Pancotti, Nicola; August, Moritz arXiv https://doi.org/10.48550/arxiv.1710.04045	text	January 2017
Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems Zeng, Tian-sheng; Zhu, W.; Sheng, D. N. arXiv https://doi.org/10.48550/arxiv.1805.01101	text	January 2018
Classical phase diagram of the stuffed honeycomb lattice Sahoo, Jyotisman; Kochkov, Dmitrii; Clark, Bryan K. arXiv https://doi.org/10.48550/arxiv.1805.09831	text	January 2018
Unifying Description of Competing Orders in Two Dimensional Quantum Magnets Song, Xue-Yang; Wang, Chong; Vishwanath, Ashvin arXiv https://doi.org/10.48550/arxiv.1811.11186	text	January 2018
Continuous phase transition between bosonic integer quantum Hall liquid and trivial insulator: evidences for deconfined quantum criticality Zeng, Tian-Sheng; Sheng, D. N.; Zhu, W. arXiv https://doi.org/10.48550/arxiv.1908.02490	text	January 2019
Determining topological order from infinite projected entangled pair states Francuz, Anna; Dziarmaga, Jacek; Vidal, Guifre arXiv https://doi.org/10.48550/arxiv.1910.09661	text	January 2019

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