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

Title: 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 ^[1]; Sheng, D. N. ^[1]

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.

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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, Vol. 4, Issue 1; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

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Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU( N ) symmetry Zeng, Tian-Sheng; Sheng, D. N.; Zhu, W. Physical Review B, Vol. 100, Issue 7 https://doi.org/10.1103/physrevb.100.075106	journal	August 2019
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
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
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 phase diagram of the spin-1 $J_{1} - J_{2}$ Heisenberg model on the honeycomb lattice Gong, Shou-Shu; Zhu, Wei; Sheng, D. N. Physical Review B, Vol. 92, Issue 19 https://doi.org/10.1103/physrevb.92.195110	journal	November 2015
Field-induced dynamical properties of the $XXZ$ model on a honeycomb lattice Maksimov, P. A.; Chernyshev, A. L. Physical Review B, Vol. 93, Issue 1 https://doi.org/10.1103/physrevb.93.014418	journal	January 2016
Theory of quantum kagome ice and vison zero modes Huang, Yi-Ping; Hermele, Michael Physical Review B, Vol. 95, Issue 7 https://doi.org/10.1103/physrevb.95.075130	journal	February 2017
Chiral topological spin liquids with projected entangled pair states Poilblanc, Didier; Cirac, J. Ignacio; Schuch, Norbert Physical Review B, Vol. 91, Issue 22 https://doi.org/10.1103/physrevb.91.224431	journal	June 2015
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
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
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
Quantum spin liquids: a review Savary, Lucile; Balents, Leon Reports on Progress in Physics, Vol. 80, Issue 1 https://doi.org/10.1088/0034-4885/80/1/016502	journal	November 2016
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
Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices Crasto de Lima, F.; Ferreira, Gerson J.; Miwa, R. H. Physical Chemistry Chemical Physics, Vol. 21, Issue 40 https://doi.org/10.1039/c9cp04760c	journal	January 2019
Lattice effects on Laughlin wave functions and parent Hamiltonians Glasser, Ivan; Cirac, J. Ignacio; Sierra, Germán Physical Review B, Vol. 94, Issue 24 https://doi.org/10.1103/physrevb.94.245104	journal	December 2016
A Kagome Map of Spin Liquids: from XXZ to Dzyaloshinskii-Moriya Ferromagnet Essafi, K.; Benton, Owen; Jaubert, Ludovic D. C. arXiv https://doi.org/10.48550/arxiv.1508.00113	text	January 2015

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