Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice
Abstract
Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. With this work, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry.We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Moreover, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Hence, we identify the liquid phase as a quantum Hall phase, which provides a “proof-of-principle” demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band.
- Authors:
-
- California State Univ. Northridge (CSUN), Northridge, CA (United States)
- Florida State Univ., Tallahassee, FL (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- California State Univ. Northridge (CSUN), Northridge, CA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1505728
- Alternate Identifier(s):
- OSTI ID: 1328624
- Grant/Contract Number:
- FG02-06ER46305
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 117; Journal Issue: 9; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Zhu, W., Gong, Shou-Shu, Zeng, Tian-Sheng, Fu, Liang, and Sheng, D. N. Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice. United States: N. p., 2016.
Web. doi:10.1103/physrevlett.117.096402.
Zhu, W., Gong, Shou-Shu, Zeng, Tian-Sheng, Fu, Liang, & Sheng, D. N. Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice. United States. https://doi.org/10.1103/physrevlett.117.096402
Zhu, W., Gong, Shou-Shu, Zeng, Tian-Sheng, Fu, Liang, and Sheng, D. N. Tue .
"Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice". United States. https://doi.org/10.1103/physrevlett.117.096402. https://www.osti.gov/servlets/purl/1505728.
@article{osti_1505728,
title = {Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice},
author = {Zhu, W. and Gong, Shou-Shu and Zeng, Tian-Sheng and Fu, Liang and Sheng, D. N.},
abstractNote = {Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. With this work, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry.We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Moreover, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Hence, we identify the liquid phase as a quantum Hall phase, which provides a “proof-of-principle” demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band.},
doi = {10.1103/physrevlett.117.096402},
journal = {Physical Review Letters},
number = 9,
volume = 117,
place = {United States},
year = {Tue Aug 23 00:00:00 EDT 2016},
month = {Tue Aug 23 00:00:00 EDT 2016}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Phases of correlated spinless fermions on the honeycomb lattice
journal, January 2014
- Daghofer, Maria; Hohenadler, Martin
- Physical Review B, Vol. 89, Issue 3
New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance
journal, August 1980
- Klitzing, K. v.; Dorda, G.; Pepper, M.
- Physical Review Letters, Vol. 45, Issue 6
Topological insulators and superconductors
journal, October 2011
- Qi, Xiao-Liang; Zhang, Shou-Cheng
- Reviews of Modern Physics, Vol. 83, Issue 4
Quantum simulation of a topological Mott insulator with Rydberg atoms in a Lieb lattice
journal, April 2016
- Dauphin, A.; Müller, M.; Martin-Delgado, M. A.
- Physical Review A, Vol. 93, Issue 4
The Quantum Anomalous Hall Effect: Theory and Experiment
journal, March 2016
- Liu, Chao-Xing; Zhang, Shou-Cheng; Qi, Xiao-Liang
- Annual Review of Condensed Matter Physics, Vol. 7, Issue 1
Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
journal, July 2009
- Sun, Kai; Yao, Hong; Fradkin, Eduardo
- Physical Review Letters, Vol. 103, Issue 4
Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
journal, August 2015
- Capponi, Sylvain; Läuchli, Andreas M.
- Physical Review B, Vol. 92, Issue 8
Interaction-driven phases in the half-filled honeycomb lattice: An infinite density matrix renormalization group study
journal, August 2015
- Motruk, Johannes; Grushin, Adolfo G.; de Juan, Fernando
- Physical Review B, Vol. 92, Issue 8
Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
journal, September 2014
- Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.
- Scientific Reports, Vol. 4, Issue 1
Interaction-Driven Topological Insulator in Fermionic Cold Atoms on an Optical Lattice: A Design with a Density Functional Formalism
journal, July 2015
- Kitamura, Sota; Tsuji, Naoto; Aoki, Hideo
- Physical Review Letters, Vol. 115, Issue 4
Interplay of charge and spin fluctuations of strongly interacting electrons on the kagome lattice
journal, July 2014
- Pollmann, Frank; Roychowdhury, Krishanu; Hotta, Chisa
- Physical Review B, Vol. 90, Issue 3
Interaction-driven fractional quantum Hall state of hard-core bosons on kagome lattice at one-third filling
journal, July 2016
- Zhu, W.; Gong, S. S.; Sheng, D. N.
- Physical Review B, Vol. 94, Issue 3
Floquet topological insulator in semiconductor quantum wells
journal, March 2011
- Lindner, Netanel H.; Refael, Gil; Galitski, Victor
- Nature Physics, Vol. 7, Issue 6
Topology by dissipation in atomic quantum wires
journal, October 2011
- Diehl, Sebastian; Rico, Enrique; Baranov, Mikhail A.
- Nature Physics, Vol. 7, Issue 12
Topological Insulators from Spontaneous Symmetry Breaking Induced by Electron Correlation on Pyrochlore Lattices
journal, April 2011
- Kurita, Moyuru; Yamaji, Youhei; Imada, Masatoshi
- Journal of the Physical Society of Japan, Vol. 80, Issue 4
Identifying topological order by entanglement entropy
journal, November 2012
- Jiang, Hong-Chen; Wang, Zhenghan; Balents, Leon
- Nature Physics, Vol. 8, Issue 12
Metal-Insulator Transition of Fermions on a Kagome Lattice at 1/3 Filling
journal, May 2010
- Nishimoto, Satoshi; Nakamura, Masaaki; O’Brien, Aroon
- Physical Review Letters, Vol. 104, Issue 19
Renormalization group study of interaction-driven quantum anomalous Hall and quantum spin Hall phases in quadratic band crossing systems
journal, May 2014
- Murray, James M.; Vafek, Oskar
- Physical Review B, Vol. 89, Issue 20
Obtaining topological degenerate ground states by the density matrix renormalization group
journal, February 2014
- He, Yin-Chen; Sheng, D. N.; Chen, Yan
- Physical Review B, Vol. 89, Issue 7
Occurrence of nematic, topological, and Berry phases when a flat and a parabolic band touch
journal, July 2014
- Dóra, Balázs; Herbut, Igor F.; Moessner, Roderich
- Physical Review B, Vol. 90, Issue 4
Density matrix formulation for quantum renormalization groups
journal, November 1992
- White, Steven R.
- Physical Review Letters, Vol. 69, Issue 19
Topological insulators in three dimensions from spontaneous symmetry breaking
journal, June 2009
- Zhang, Yi; Ran, Ying; Vishwanath, Ashvin
- Physical Review B, Vol. 79, Issue 24
Quantum anomalous Hall state in bilayer graphene
journal, September 2010
- Nandkishore, Rahul; Levitov, Leonid
- Physical Review B, Vol. 82, Issue 11
Fractional Chern insulators in bands with zero Berry curvature
journal, November 2015
- Simon, Steven H.; Harper, Fenner; Read, N.
- Physical Review B, Vol. 92, Issue 19
Interaction-driven phases in the half-filled spinless honeycomb lattice from exact diagonalization
journal, December 2013
- García-Martínez, Noel A.; Grushin, Adolfo G.; Neupert, Titus
- Physical Review B, Vol. 88, Issue 24
Possible interaction-driven topological phases in (111) bilayers of LaNiO
journal, November 2011
- Yang, Kai-Yu; Zhu, Wenguang; Xiao, Di
- Physical Review B, Vol. 84, Issue 20
Topological insulators from complex orbital order in transition-metal oxides heterostructures
journal, November 2011
- Rüegg, Andreas; Fiete, Gregory A.
- Physical Review B, Vol. 84, Issue 20
Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
journal, August 2010
- Wen, Jun; Rüegg, Andreas; Wang, C. -C. Joseph
- Physical Review B, Vol. 82, Issue 7
Fractional Quantum Hall States at Zero Magnetic Field
journal, June 2011
- Neupert, Titus; Santos, Luiz; Chamon, Claudio
- Physical Review Letters, Vol. 106, Issue 23
Instabilities of quadratic band crossing points
journal, November 2011
- Uebelacker, Stefan; Honerkamp, Carsten
- Physical Review B, Vol. 84, Issue 20
High-Temperature Fractional Quantum Hall States
journal, June 2011
- Tang, Evelyn; Mei, Jia-Wei; Wen, Xiao-Gang
- Physical Review Letters, Vol. 106, Issue 23
Nearly Flatbands with Nontrivial Topology
journal, June 2011
- Sun, Kai; Gu, Zhengcheng; Katsura, Hosho
- Physical Review Letters, Vol. 106, Issue 23
Band touching from real-space topology in frustrated hopping models
journal, September 2008
- Bergman, Doron L.; Wu, Congjun; Balents, Leon
- Physical Review B, Vol. 78, Issue 12
Topological Mott Insulators
journal, April 2008
- Raghu, S.; Qi, Xiao-Liang; Honerkamp, C.
- Physical Review Letters, Vol. 100, Issue 15
Ultracold Atoms in a Tunable Optical Kagome Lattice
journal, January 2012
- Jo, Gyu-Boong; Guzman, Jennie; Thomas, Claire K.
- Physical Review Letters, Vol. 108, Issue 4
Chiral spin states and superconductivity
journal, June 1989
- Wen, X. G.; Wilczek, Frank; Zee, A.
- Physical Review B, Vol. 39, Issue 16
Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
journal, March 2013
- Chang, C. -Z.; Zhang, J.; Feng, X.
- Science, Vol. 340, Issue 6129
Interaction-driven instabilities of a Dirac semimetal
journal, February 2010
- Weeks, C.; Franz, M.
- Physical Review B, Vol. 81, Issue 8
Macroscopic Magnetization Jumps due to Independent Magnons in Frustrated Quantum Spin Lattices
journal, April 2002
- Schulenburg, J.; Honecker, A.; Schnack, J.
- Physical Review Letters, Vol. 88, Issue 16
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
Quantum Spin Hall Effect in Graphene
journal, November 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 22
Colloquium: Topological insulators
journal, November 2010
- Hasan, M. Z.; Kane, C. L.
- Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067
Characterization and stability of a fermionic fractional Chern insulator
journal, January 2015
- Grushin, Adolfo G.; Motruk, Johannes; Zaletel, Michael P.
- Physical Review B, Vol. 91, Issue 3
Flux insertion, entanglement, and quantized responses
journal, October 2014
- Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 10
Experimental realization of the topological Haldane model with ultracold fermions
journal, November 2014
- Jotzu, Gregor; Messer, Michael; Desbuquois, Rémi
- Nature, Vol. 515, Issue 7526
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988
- Haldane, F. D. M.
- Physical Review Letters, Vol. 61, Issue 18
Topological flat band Models and Fractional Chern Insulators
journal, September 2013
- Bergholtz, Emil J.; Liu, Zhao
- International Journal of Modern Physics B, Vol. 27, Issue 24
Disorder-Driven Collapse of the Mobility Gap and Transition to an Insulator in the Fractional Quantum Hall Effect
journal, June 2003
- Sheng, D. N.; Wan, Xin; Rezayi, E. H.
- Physical Review Letters, Vol. 90, Issue 25
Characterizing Topological Order by Studying the Ground States on an Infinite Cylinder
journal, February 2013
- Cincio, L.; Vidal, G.
- Physical Review Letters, Vol. 110, Issue 6
Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels
journal, December 2011
- Kitagawa, Takuya; Oka, Takashi; Brataas, Arne
- Physical Review B, Vol. 84, Issue 23
Quantized Hall conductivity in two dimensions
journal, May 1981
- Laughlin, R. B.
- Physical Review B, Vol. 23, Issue 10
Topological characterization of the non-Abelian Moore-Read state using density-matrix renormalization group
journal, October 2015
- Zhu, W.; Gong, S. S.; Haldane, F. D. M.
- Physical Review B, Vol. 92, Issue 16
Quantum Spin-Hall Effect and Topologically Invariant Chern Numbers
journal, July 2006
- Sheng, D. N.; Weng, Z. Y.; Sheng, L.
- Physical Review Letters, Vol. 97, Issue 3
Interaction-driven topological and nematic phases on the Lieb lattice
journal, May 2015
- Tsai, Wei-Feng; Fang, Chen; Yao, Hong
- New Journal of Physics, Vol. 17, Issue 5
Flat Bands and Wigner Crystallization in the Honeycomb Optical Lattice
journal, August 2007
- Wu, Congjun; Bergman, Doron; Balents, Leon
- Physical Review Letters, Vol. 99, Issue 7
Dynamic Generation of Spin-Orbit Coupling
journal, July 2004
- Wu, Congjun; Zhang, Shou-Cheng
- Physical Review Letters, Vol. 93, Issue 3
Fractional quantum Hall effect in the absence of Landau levels
journal, July 2011
- Sheng, D. N.; Gu, Zheng-Cheng; Sun, Kai
- Nature Communications, Vol. 2, Issue 1
Works referencing / citing this record:
Tuning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
journal, September 2018
- Zeng, Tian-Sheng; Zhu, Wei; Sheng, Donna
- npj Quantum Materials, Vol. 3, Issue 1
Giant and anisotropic many-body spin–orbit tunability in a strongly correlated kagome magnet
journal, September 2018
- Yin, Jia-Xin; Zhang, Songtian S.; Li, Hang
- Nature, Vol. 562, Issue 7725
Phase diagram of interacting spinless fermions on the honeycomb lattice
journal, November 2016
- Capponi, Sylvain
- Journal of Physics: Condensed Matter, Vol. 29, Issue 4
Interacting topological insulators: a review
journal, October 2018
- Rachel, Stephan
- Reports on Progress in Physics, Vol. 81, Issue 11
Measuring an interaction-induced topological phase transition via the single-particle density matrix
journal, January 2020
- Zheng, Jun-Hui; Irsigler, Bernhard; Jiang, Lijia
- Physical Review A, Vol. 101, Issue 1
Chiral spin liquid with spinon Fermi surfaces in the spin- triangular Heisenberg model
journal, December 2019
- Gong, Shou-Shu; Zheng, Wayne; Lee, Mac
- Physical Review B, Vol. 100, Issue 24
Large-gap quantum anomalous Hall phase in hexagonal organometallic frameworks
journal, December 2018
- Jin, Yuanjun; Chen, Zhongjia; Xia, Bowen
- Physical Review B, Vol. 98, Issue 24
Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching
journal, December 2018
- Ray, Shouryya; Vojta, Matthias; Janssen, Lukas
- Physical Review B, Vol. 98, Issue 24
Symmetry-breaking topological insulators in the Bose-Hubbard model
journal, January 2019
- González-Cuadra, Daniel; Dauphin, Alexandre; Grzybowski, Przemysław R.
- Physical Review B, Vol. 99, Issue 4
Phase diagram of interacting spinless fermions on the honeycomb lattice
text, January 2016
- Capponi, Sylvain
- arXiv
Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
text, January 2018
- Zeng, Tian-sheng; Zhu, W.; Sheng, D. N.
- arXiv
Giant and anisotropic many-body spin-orbit tunability in a strongly correlated kagome magnet
text, January 2018
- Yin, Jia-Xin; Zhang, Songtian S.; Li, Hang
- arXiv
Large Band Gap Quantum Anomalous Hall Phase in Hexagonal Organometallic Frameworks
text, January 2018
- Jin, Yuanjun; Chen, Zhongjia; Xia, Bowen
- arXiv
Figures / Tables found in this record: