Chiral spin liquid with spinon Fermi surfaces in the spin-$\frac{1}{2}$ triangular Heisenberg model

Gong, Shou-Shu; Zheng, Wayne; Lee, Mac; Lu, Yuan-Ming; Sheng, D. N.

doi:10.1103/physrevb.100.241111

Chiral spin liquid with spinon Fermi surfaces in the spin-$$\frac{1}{2}$$ triangular Heisenberg model

Journal Article · Mon Dec 16 00:00:00 EST 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.100.241111· OSTI ID:1800369

^[1]; Zheng, Wayne ^[2]; Lee, Mac ^[3]; Lu, Yuan-Ming ^[2]; Sheng, D. N. ^[4]

Beihang University, Beijing (China)
The Ohio State Univ., Columbus, OH (United States)
California State Univ., Northridge, CA (United States); Univ. of California, San Diego, CA (United States)
California State Univ., Northridge, CA (United States)

Here, we study the interplay of competing interactions in spin-$$\frac{1}{2}$$ triangular Heisenberg model through tuning the first- ($$J_1$$), second- ($$J_2$$), and third-neighbor ($$J_ 3$$) couplings. Based on a large-scale density-matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a gapless chiral spin-liquid (CSL) phase in the intermediate $$J_2$$ and $$J_ 3$$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin-liquid state, the U(1) staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the U(1) Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero $$J_2$$ and $$J_3$$, which naturally explains the numerical results. This realizes an example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of interesting quantum phases emergent from competing interactions in triangular-lattice magnets.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: National Natural Science Foundation of China (NSFC); Fundamental Research Funds for the Central Universities; National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-06ER46305; 11874078; 11834014; DMR-1828019; DMR-1653769

OSTI ID:: 1800369

Journal Information:: Physical Review. B, Vol. 100, Issue 24; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (90)

The non-Abelian density matrix renormalization group algorithm McCulloch, I. P.; Gulácsi, M. Europhysics Letters (EPL), Vol. 57, Issue 6 https://doi.org/10.1209/epl/i2002-00393-0	journal	March 2002
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
Thermodynamic properties of a spin-1/2 spin-liquid state in a κ-type organic salt Yamashita, Satoshi; Nakazawa, Yasuhiro; Oguni, Masaharu Nature Physics, Vol. 4, Issue 6 https://doi.org/10.1038/nphys942	journal	April 2008
Spinon Fermi surface U ( 1 ) spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator YbMgGaO 4 Li, Yao-Dong; Lu, Yuan-Ming; Chen, Gang Physical Review B, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevB.96.054445	journal	August 2017
Quasiclassical magnetic order and its loss in a spin- 1 2 Heisenberg antiferromagnet on a triangular lattice with competing bonds Li, P. H. Y.; Bishop, R. F.; Campbell, C. E. Physical Review B, Vol. 91, Issue 1 https://doi.org/10.1103/PhysRevB.91.014426	journal	January 2015
Magnetic Interactions in the Geometrically Frustrated Triangular Lattice Antiferromagnet CuFeO 2 Ye, F.; Fernandez-Baca, J. A.; Fishman, R. S. Physical Review Letters, Vol. 99, Issue 15 https://doi.org/10.1103/PhysRevLett.99.157201	journal	October 2007
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
Quantum orders and symmetric spin liquids Wen, Xiao-Gang Physical Review B, Vol. 65, Issue 16 https://doi.org/10.1103/PhysRevB.65.165113	journal	April 2002
Competing spin-liquid states in the spin- 1 2 Heisenberg model on the triangular lattice Hu, Wen-Jun; Gong, Shou-Shu; Zhu, Wei Physical Review B, Vol. 92, Issue 14 https://doi.org/10.1103/PhysRevB.92.140403	journal	October 2015
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
Thermal-transport measurements in a quantum spin-liquid state of the frustrated triangular magnet κ-(BEDT-TTF)2Cu2(CN)3 Yamashita, Minoru; Nakata, Norihito; Kasahara, Yuichi Nature Physics, Vol. 5, Issue 1 https://doi.org/10.1038/nphys1134	journal	November 2008
Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet Yan, S.; Huse, D. A.; White, S. R. Science, Vol. 332, Issue 6034 https://doi.org/10.1126/science.1201080	journal	April 2011
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
Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States Li, Hui; Haldane, F. D. M. Physical Review Letters, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevLett.101.010504	journal	July 2008
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
Spiral phases in easy plane J1-J2-J3 triangular antiferromagnets Ivanov, N. B.; Richter, J. Journal of Magnetism and Magnetic Materials, Vol. 140-144 https://doi.org/10.1016/0304-8853(94)00530-3	journal	February 1995
A new high-temperature quantum spin liquid with polaron spins Klanjsek, Martin; Zorko, Andrej; Zitko, Rok arXiv https://doi.org/10.48550/arxiv.1704.06450	text	January 2017
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
Anyons in an exactly solved model and beyond Kitaev, Alexei arXiv https://doi.org/10.48550/arxiv.cond-mat/0506438	text	January 2005
Spin Bose-metal phase in a spin- 1 2 model with ring exchange on a two-leg triangular strip Sheng, D. N.; Motrunich, Olexei I.; Fisher, Matthew P. A. Physical Review B, Vol. 79, Issue 20 https://doi.org/10.1103/PhysRevB.79.205112	journal	May 2009
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
Fractionalization in the cuprates: Detecting the topological order Senthil, T.; Fisher, Matthew P. A. arXiv https://doi.org/10.48550/arxiv.cond-mat/0006481	text	January 2000
A quantum dipolar spin liquid Yao, N. Y.; Zaletel, M. P.; Stamper-Kurn, D. M. Nature Physics, Vol. 14, Issue 4 https://doi.org/10.1038/s41567-017-0030-7	journal	February 2018
Density matrix formulation for quantum renormalization groups White, Steven R. Physical Review Letters, Vol. 69, Issue 19 https://doi.org/10.1103/PhysRevLett.69.2863	journal	November 1992
Spin liquid nature in the Heisenberg J 1 − J 2 triangular antiferromagnet Iqbal, Yasir; Hu, Wen-Jun; Thomale, Ronny Physical Review B, Vol. 93, Issue 14 https://doi.org/10.1103/PhysRevB.93.144411	journal	April 2016
Large- N expansion for frustrated quantum antiferromagnets Read, N.; Sachdev, Subir Physical Review Letters, Vol. 66, Issue 13 https://doi.org/10.1103/PhysRevLett.66.1773	journal	April 1991
Neutron powder diffraction study of the two-dimensional triangular lattice antiferromagnet CuCrO ₂ Kadowaki, H.; Kikuchi, H.; Ajiro, Y. Journal of Physics: Condensed Matter, Vol. 2, Issue 19 https://doi.org/10.1088/0953-8984/2/19/014	journal	May 1990
Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice Misguich, Gregoire; Lhuillier, Claire; Bernu, Bernard arXiv https://doi.org/10.48550/arxiv.cond-mat/9812329	text	January 1998
Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons Sachdev, Subir Physical Review B, Vol. 45, Issue 21 https://doi.org/10.1103/PhysRevB.45.12377	journal	June 1992
1T-TaS ₂ as a quantum spin liquid Law, K. T.; Lee, Patrick A. Proceedings of the National Academy of Sciences, Vol. 114, Issue 27 https://doi.org/10.1073/pnas.1706769114	journal	June 2017
Unifying description of competing orders in two-dimensional quantum magnets Song, Xue-Yang; Wang, Chong; Vishwanath, Ashvin Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-11727-3	journal	September 2019
Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice Iaconis, Jason; Liu, Chunxiao; Halász, Gábor B. arXiv https://doi.org/10.48550/arxiv.1708.07856	text	January 2017
Z 2 gauge theory of electron fractionalization in strongly correlated systems Senthil, T.; Fisher, Matthew P. A. Physical Review B, Vol. 62, Issue 12 https://doi.org/10.1103/PhysRevB.62.7850	journal	September 2000
Inversion-symmetry breaking in the noncollinear magnetic phase of the triangular-lattice antiferromagnet Cu Fe O 2 Kimura, T.; Lashley, J. C.; Ramirez, A. P. Physical Review B, Vol. 73, Issue 22 https://doi.org/10.1103/PhysRevB.73.220401	journal	June 2006
Projective symmetry group classification of chiral spin liquids Bieri, Samuel; Lhuillier, Claire; Messio, Laura Physical Review B, Vol. 93, Issue 9 https://doi.org/10.1103/PhysRevB.93.094437	journal	March 2016
Dirac Spin Liquid on the Spin- 1 / 2 Triangular Heisenberg Antiferromagnet Hu, Shijie; Zhu, W.; Eggert, Sebastian Physical Review Letters, Vol. 123, Issue 20 https://doi.org/10.1103/PhysRevLett.123.207203	journal	November 2019
Quantum Spin Liquid States Zhou, Yi; Kanoda, Kazushi; Ng, Tai-Kai arXiv https://doi.org/10.48550/arxiv.1607.03228	text	January 2016
Kapellasite: A Kagome Quantum Spin Liquid with Competing Interactions Fåk, B.; Kermarrec, E.; Messio, L. Physical Review Letters, Vol. 109, Issue 3 https://doi.org/10.1103/PhysRevLett.109.037208	journal	July 2012
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
Spin liquids in frustrated magnets Balents, Leon Nature, Vol. 464, Issue 7286 https://doi.org/10.1038/nature08917	journal	March 2010
Anyons in an exactly solved model and beyond Kitaev, Alexei Annals of Physics, Vol. 321, Issue 1 https://doi.org/10.1016/j.aop.2005.10.005	journal	January 2006
Topography of Spin Liquids on a Triangular Lattice Zhu, Zhenyue; Maksimov, P. A.; White, Steven R. Physical Review Letters, Vol. 120, Issue 20 https://doi.org/10.1103/PhysRevLett.120.207203	journal	May 2018
Gapless excitations in the ground state of 1 T − TaS 2 Ribak, A.; Silber, I.; Baines, C. Physical Review B, Vol. 96, Issue 19 https://doi.org/10.1103/PhysRevB.96.195131	journal	November 2017
Magnetic Interaction in the Geometrically Frustrated Triangular Lattice Antiferromagnet $\rm CuFeO_2$ Ye, F.; Fernandez-Baca, J. A.; Fishman, R. S. arXiv https://doi.org/10.48550/arxiv.0708.1198	text	January 2007
The Non-Abelian Density Matrix Renormalization Group Algorithm McCulloch, I.; Gulacsi, M. arXiv https://doi.org/10.48550/arxiv.cond-mat/0012319	text	January 2000
Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4 Shen, Yao; Li, Yao-Dong; Walker, H. C. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-06588-1	journal	October 2018
Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model Kaneko, Ryui; Morita, Satoshi; Imada, Masatoshi arXiv https://doi.org/10.48550/arxiv.1407.0318	text	January 2014
Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections Hermanns, M.; Kimchi, I.; Knolle, J. Annual Review of Condensed Matter Physics, Vol. 9, Issue 1 https://doi.org/10.1146/annurev-conmatphys-033117-053934	journal	March 2018
Variational study of triangular lattice spin- 1 ∕ 2 model with ring exchanges and spin liquid state in κ − ( ET ) 2 Cu 2 ( CN ) 3 Motrunich, Olexei I. Physical Review B, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevB.72.045105	journal	July 2005
Hierarchy of exchange interactions in the triangular-lattice spin-liquid YbMgGaO$_{4}$ Zhang, Xinshu; Mahmood, Fahad; Daum, Marcus arXiv https://doi.org/10.48550/arxiv.1708.07503	text	January 2017
The half-filled Landau level: The case for Dirac composite fermions Geraedts, S. D.; Zaletel, M. P.; Mong, R. S. K. Science, Vol. 352, Issue 6282 https://doi.org/10.1126/science.aad4302	journal	April 2016
Mean-field theory of spin-liquid states with finite energy gap and topological orders Wen, X. G. Physical Review B, Vol. 44, Issue 6 https://doi.org/10.1103/PhysRevB.44.2664	journal	August 1991
The half-filled Landau level: the case for Dirac composite fermions Geraedts, Scott D.; Zaletel, Michael P.; Mong, Roger S. K. arXiv https://doi.org/10.48550/arxiv.1508.04140	text	January 2015
Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice Zhu, W.; Gong, Shou-Shu; Zeng, Tian-Sheng Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.096402	journal	August 2016
Highly Mobile Gapless Excitations in a Two-Dimensional Candidate Quantum Spin Liquid Yamashita, M.; Nakata, N.; Senshu, Y. Science, Vol. 328, Issue 5983 https://doi.org/10.1126/science.1188200	journal	June 2010
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
Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4 Paddison, Joseph A. M.; Daum, Marcus; Dun, Zhiling Nature Physics, Vol. 13, Issue 2 https://doi.org/10.1038/nphys3971	journal	December 2016
Rare-Earth Triangular Lattice Spin Liquid: A Single-Crystal Study of YbMgGaO 4 Li, Yuesheng; Chen, Gang; Tong, Wei Physical Review Letters, Vol. 115, Issue 16 https://doi.org/10.1103/PhysRevLett.115.167203	journal	October 2015
Spin liquid phase of the S = 1 2 J 1 − J 2 Heisenberg model on the triangular lattice Zhu, Zhenyue; White, Steven R. Physical Review B, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevB.92.041105	journal	July 2015
Normal-state properties of the uniform resonating-valence-bond state Nagaosa, Naoto; Lee, Patrick A. Physical Review Letters, Vol. 64, Issue 20 https://doi.org/10.1103/PhysRevLett.64.2450	journal	May 1990
Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor κ − ( ET ) 2 Cu 2 ( CN ) 3 Kurosaki, Y.; Shimizu, Y.; Miyagawa, K. Physical Review Letters, Vol. 95, Issue 17 https://doi.org/10.1103/PhysRevLett.95.177001	journal	October 2005
Symmetry fractionalization in the topological phase of the spin- 1 2 J 1 − J 2 triangular Heisenberg model Saadatmand, S. N.; McCulloch, I. P. Physical Review B, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevB.94.121111	journal	September 2016
Fractionalization in the Cuprates: Detecting the Topological Order Fisher, Matthew P. A.; Senthil, T. The American Physical Society https://doi.org/10.17877/de290r-11971	text	January 2001
Gauge theory of the normal state of high- T c superconductors Lee, Patrick A.; Nagaosa, Naoto Physical Review B, Vol. 46, Issue 9 https://doi.org/10.1103/PhysRevB.46.5621	journal	September 1992
Heat transport study of the spin liquid candidate 1 T − TaS 2 Yu, Y. J.; Xu, Y.; He, L. P. Physical Review B, Vol. 96, Issue 8 https://doi.org/10.1103/PhysRevB.96.081111	journal	August 2017
Investigation of the chiral antiferromagnetic Heisenberg model using projected entangled pair states Poilblanc, Didier Physical Review B, Vol. 96, Issue 12 https://doi.org/10.1103/PhysRevB.96.121118	journal	September 2017
Resonating valence bonds: A new kind of insulator? Anderson, P. W. Materials Research Bulletin, Vol. 8, Issue 2 https://doi.org/10.1016/0025-5408(73)90167-0	journal	February 1973
Gapless fermions and gauge fields in dielectrics Ioffe, L. B.; Larkin, A. I. Physical Review B, Vol. 39, Issue 13 https://doi.org/10.1103/PhysRevB.39.8988	journal	May 1989
Symmetric Z 2 spin liquids and their neighboring phases on triangular lattice Lu, Yuan-Ming Physical Review B, Vol. 93, Issue 16 https://doi.org/10.1103/PhysRevB.93.165113	journal	April 2016
Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice Misguich, G.; Lhuillier, C.; Bernu, B. Physical Review B, Vol. 60, Issue 2 https://doi.org/10.1103/PhysRevB.60.1064	journal	July 1999
Spinon Fermi Surface in a Cluster Mott Insulator Model on a Triangular Lattice and Possible Application to 1 T − Ta S 2 He, Wen-Yu; Xu, Xiao Yan; Chen, Gang Physical Review Letters, Vol. 121, Issue 4 https://doi.org/10.1103/PhysRevLett.121.046401	journal	July 2018
Electron scattering on magnetic impurities in metals and anomalous resistivity effects Abrikosov, A. A. Physics Physique Fizika, Vol. 2, Issue 1 https://doi.org/10.1103/PhysicsPhysiqueFizika.2.5	journal	September 1965
Doping a Mott insulator: Physics of high-temperature superconductivity Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang Reviews of Modern Physics, Vol. 78, Issue 1 https://doi.org/10.1103/RevModPhys.78.17	journal	January 2006
Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension Dubail, J.; Read, N. Physical Review B, Vol. 92, Issue 20 https://doi.org/10.1103/PhysRevB.92.205307	journal	November 2015
Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO 4 Zhang, Xinshu; Mahmood, Fahad; Daum, Marcus Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031001	journal	July 2018
Spin Bose-Metal and Valence Bond Solid Phases in a Spin- 1 / 2 Model with Ring Exchanges on a Four-Leg Triangular Ladder Block, Matthew S.; Sheng, D. N.; Motrunich, Olexei I. Physical Review Letters, Vol. 106, Issue 15 https://doi.org/10.1103/PhysRevLett.106.157202	journal	April 2011
Fractionalization in the Cuprates: Detecting the Topological Order Senthil, T.; Fisher, Matthew P. A. Physical Review Letters, Vol. 86, Issue 2 https://doi.org/10.1103/PhysRevLett.86.292	journal	January 2001
A high-temperature quantum spin liquid with polaron spins Klanjšek, Martin; Zorko, Andrej; Žitko, Rok Nature Physics, Vol. 13, Issue 11 https://doi.org/10.1038/nphys4212	journal	July 2017
Spin-Driven Ferroelectricity in Triangular Lattice Antiferromagnets A CrO 2 ( A = Cu , Ag, Li, or Na) Seki, S.; Onose, Y.; Tokura, Y. Physical Review Letters, Vol. 101, Issue 6 https://doi.org/10.1103/PhysRevLett.101.067204	journal	August 2008
Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4 Paddison, J. A. M.; Daum, M.; Dun, Z. L. arXiv https://doi.org/10.48550/arxiv.1607.03231	text	January 2016
Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice Iaconis, Jason; Liu, Chunxiao; Halász, Gábor SciPost Physics, Vol. 4, Issue 1 https://doi.org/10.21468/SciPostPhys.4.1.003	journal	January 2018
Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons Wen, Xiao-Gang ISRN Condensed Matter Physics, Vol. 2013 https://doi.org/10.1155/2013/198710	journal	January 2013
Symmetry fractionalization in the topological phase of the spin-$\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model Saadatmand, S. N.; McCulloch, I. P. arXiv https://doi.org/10.48550/arxiv.1606.00334	text	January 2016
Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice Shimizu, Y.; Miyagawa, K.; Kanoda, K. Physical Review Letters, Vol. 91, Issue 10 https://doi.org/10.1103/PhysRevLett.91.107001	journal	September 2003
Fractionalization in the Cuprates: Detecting the Topological Order Senthil, T.; Fisher, M. P. A. Topologica, Vol. 1, Issue 1 https://doi.org/10.3731/topologica.1.010	journal	January 2008
Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections Hermanns, Maria; Kimchi, Itamar; Knolle, Johannes Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.10431	text	January 2018
Gapless Spin-Liquid Phase in an Extended Spin 1/2 Triangular Heisenberg Model Kaneko, Ryui; Morita, Satoshi; Imada, Masatoshi Journal of the Physical Society of Japan, Vol. 83, Issue 9 https://doi.org/10.7566/JPSJ.83.093707	journal	September 2014
The evolution and breakdown of submesoscale instabilities Stamper, Megan Andrena Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.25162	text	January 2018
Spin-driven ferroelectricity and possible antiferroelectricity in triangular lattice antiferromagnets ACrO2 (A = Cu, Ag, Li, or Na) Seki, S.; Onose, Y.; Tokura, Y. arXiv https://doi.org/10.48550/arxiv.0801.3757	text	January 2008
Quantum Spin Liquids Savary, Lucile; Balents, Leon arXiv https://doi.org/10.48550/arxiv.1601.03742	text	January 2016

Similar Records

Quantum spin liquid with emergent chiral order in the triangular-lattice Hubbard model

Journal Article · Fri Sep 16 00:00:00 EDT 2022 · Physical Review. B · OSTI ID:1886240

Chen, Bin-Bin; Chen, Ziyu; Gong, Shou-Shu; +3 more

Spectral function of the $J_1$ – $J_2$ Heisenberg model on the triangular lattice

Journal Article · Tue Apr 25 00:00:00 EDT 2023 · Physical Review. B · OSTI ID:2234154

Sherman, Nicholas E.; Dupont, Maxime; Moore, Joel E.

Nematic spin liquid phase in a frustrated spin-1 system on the square lattice

Journal Article · Mon Oct 28 00:00:00 EDT 2019 · Physical Review. B · OSTI ID:1803293

Hu, Wen-Jun; Gong, Shou-Shu; Lai, Hsin-Hua; +3 more

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Materials Science
Physics

Chiral spin liquid with spinon Fermi surfaces in the spin-$$\frac{1}{2}$$ triangular Heisenberg model

Citation Formats

References (90)

Similar Records

Related Subjects