Doped Mott insulators in the triangular-lattice Hubbard model
Abstract
Here we investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping δ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping δ ≲ 10%, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, δ ≈ 10%~20% SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping δ ≳ 20%, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.
- Authors:
-
- Harvard University, Cambridge, MA (United States); Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing China)
- California State University, Northridge (CSUN), CA (United States)
- Harvard University, Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- California State Univ. (CalState), Long Beach, CA (United States); California State University, Northridge (CSUN), CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); National Natural Science Foundation of China (NSFC); Central Universities; Chinese Academy of Sciences; Simons Foundation
- OSTI Identifier:
- 1979761
- Alternate Identifier(s):
- OSTI ID: 2203492
- Grant/Contract Number:
- FG02-06ER46305; 12074375; E0EG4303X2; 118900M026; XDB33000000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 105; Journal Issue: 20; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; frustrated magnetism; spin density waves; Mott insulators; strongly correlated systems; density matrix renormalization group
Citation Formats
Zhu, Zheng, Sheng, D. N., and Vishwanath, Ashvin. Doped Mott insulators in the triangular-lattice Hubbard model. United States: N. p., 2022.
Web. doi:10.1103/physrevb.105.205110.
Zhu, Zheng, Sheng, D. N., & Vishwanath, Ashvin. Doped Mott insulators in the triangular-lattice Hubbard model. United States. https://doi.org/10.1103/physrevb.105.205110
Zhu, Zheng, Sheng, D. N., and Vishwanath, Ashvin. Tue .
"Doped Mott insulators in the triangular-lattice Hubbard model". United States. https://doi.org/10.1103/physrevb.105.205110. https://www.osti.gov/servlets/purl/1979761.
@article{osti_1979761,
title = {Doped Mott insulators in the triangular-lattice Hubbard model},
author = {Zhu, Zheng and Sheng, D. N. and Vishwanath, Ashvin},
abstractNote = {Here we investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping δ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping δ ≲ 10%, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, δ ≈ 10%~20% SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping δ ≳ 20%, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.},
doi = {10.1103/physrevb.105.205110},
journal = {Physical Review. B},
number = 20,
volume = 105,
place = {United States},
year = {Tue May 10 00:00:00 EDT 2022},
month = {Tue May 10 00:00:00 EDT 2022}
}
Works referenced in this record:
Spin-liquid versus spiral-order phases in the anisotropic triangular lattice
journal, January 2013
- Tocchio, Luca F.; Feldner, Hélène; Becca, Federico
- Physical Review B, Vol. 87, Issue 3
Hidden spin current in doped Mott antiferromagnets
journal, October 2018
- Zheng, Wayne; Zhu, Zheng; Sheng, D. N.
- Physical Review B, Vol. 98, Issue 16
Localization in a
t − J
-Type Model with Translational Symmetry
journal, July 2019
- Sun, Rong-Yang; Zhu, Zheng; Weng, Zheng-Yu
- Physical Review Letters, Vol. 123, Issue 1
Unconventional superconductivity on the triangular lattice Hubbard model
journal, July 2013
- Chen, Kuang Shing; Meng, Zi Yang; Yu, Unjong
- Physical Review B, Vol. 88, Issue 4
Hubbard Model Physics in Transition Metal Dichalcogenide Moiré Bands
journal, July 2018
- Wu, Fengcheng; Lovorn, Timothy; Tutuc, Emanuel
- Physical Review Letters, Vol. 121, Issue 2
Metal-Insulator Transition in the Hubbard Model on a Triangular Lattice
journal, July 1991
- Jayaprakash, C.; Krishnamurthy, H. R.; Sarker, S.
- Europhysics Letters (EPL), Vol. 15, Issue 6
Intrinsic translational symmetry breaking in a doped Mott insulator
journal, July 2018
- Zhu, Zheng; Sheng, D. N.; Weng, Zheng-Yu
- Physical Review B, Vol. 98, Issue 3
Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
journal, March 2017
- Ehlers, G.; White, S. R.; Noack, R. M.
- Physical Review B, Vol. 95, Issue 12
Quantum spin liquids: a review
journal, November 2016
- Savary, Lucile; Balents, Leon
- Reports on Progress in Physics, Vol. 80, Issue 1
Phase diagram of the anisotropic triangular lattice Hubbard model
journal, June 2021
- Szasz, Aaron; Motruk, Johannes
- Physical Review B, Vol. 103, Issue 23
Effective Spin Model for the Spin-Liquid Phase of the Hubbard Model on the Triangular Lattice
journal, December 2010
- Yang, Hong-Yu; Läuchli, Andreas M.; Mila, Frédéric
- Physical Review Letters, Vol. 105, Issue 26
Equivalence of the resonating-valence-bond and fractional quantum Hall states
journal, November 1987
- Kalmeyer, V.; Laughlin, R. B.
- Physical Review Letters, Vol. 59, Issue 18
Quantum spin liquid states
journal, April 2017
- Zhou, Yi; Kanoda, Kazushi; Ng, Tai-Kai
- Reviews of Modern Physics, Vol. 89, Issue 2
Mott transition on a triangular lattice
journal, March 2009
- Galanakis, Dimitrios; Stanescu, Tudor D.; Phillips, Philip
- Physical Review B, Vol. 79, Issue 11
Density-matrix algorithms for quantum renormalization groups
journal, October 1993
- White, Steven R.
- Physical Review B, Vol. 48, Issue 14
Field-tunable quantum disordered ground state in the triangular-lattice antiferromagnet NaYbO2
journal, July 2019
- Bordelon, Mitchell M.; Kenney, Eric; Liu, Chunxiao
- Nature Physics, Vol. 15, Issue 10
Ground-state phase diagram of the triangular lattice Hubbard model by the density-matrix renormalization group method
journal, November 2017
- Shirakawa, Tomonori; Tohyama, Takami; Kokalj, Jure
- Physical Review B, Vol. 96, Issue 20
Doped model on a triangular lattice: Possible application to and
journal, March 2004
- Wang, Qiang-Hua; Lee, Dung-Hai; Lee, Patrick A.
- Physical Review B, Vol. 69, Issue 9
Magnetic properties and Mott transition in the Hubbard model on the anisotropic triangular lattice
journal, May 2014
- Yamada, A.
- Physical Review B, Vol. 89, Issue 19
Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study
journal, May 2020
- Szasz, Aaron; Motruk, Johannes; Zaletel, Michael P.
- Physical Review X, Vol. 10, Issue 2
Study of the triangular latticet V model nearx = 1 3
journal, July 2004
- Motrunich, O. I.; Lee, Patrick A.
- Physical Review B, Vol. 70, Issue 2
Density matrix formulation for quantum renormalization groups
journal, November 1992
- White, Steven R.
- Physical Review Letters, Vol. 69, Issue 19
One-dimensional spin liquid, collinear, and spiral phases from uncoupled chains to the triangular lattice
journal, June 2014
- Tocchio, Luca F.; Gros, Claudius; Valentí, Roser
- Physical Review B, Vol. 89, Issue 23
Spin liquid nature in the Heisenberg triangular antiferromagnet
journal, April 2016
- Iqbal, Yasir; Hu, Wen-Jun; Thomale, Ronny
- Physical Review B, Vol. 93, Issue 14
Electronic Model for Layer Based Systems: Chiral Resonating Valence Bond Metal and Superconductivity
journal, August 2003
- Baskaran, G.
- Physical Review Letters, Vol. 91, Issue 9
Instability of a quantum spin liquid in an organic triangular-lattice antiferromagnet
journal, July 2010
- Itou, T.; Oyamada, A.; Maegawa, S.
- Nature Physics, Vol. 6, Issue 9
Site-Resolved Imaging of Ultracold Fermions in a Triangular-Lattice Quantum Gas Microscope
journal, June 2021
- Yang, Jin; Liu, Liyu; Mongkolkiattichai, Jirayu
- PRX Quantum, Vol. 2, Issue 2
Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons
journal, June 1992
- Sachdev, Subir
- Physical Review B, Vol. 45, Issue 21
Spin-liquid states on the triangular and Kagomé lattices: A projective-symmetry-group analysis of Schwinger boson states
journal, November 2006
- Wang, Fa; Vishwanath, Ashvin
- Physical Review B, Vol. 74, Issue 17
Competing phases of the Hubbard model on a triangular lattice: Insights from the entropy
journal, April 2014
- Li, Gang; Antipov, Andrey E.; Rubtsov, Alexey N.
- Physical Review B, Vol. 89, Issue 16
1T-TaS 2 as a quantum spin liquid
journal, June 2017
- Law, K. T.; Lee, Patrick A.
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 27
Unifying description of competing orders in two-dimensional quantum magnets
journal, September 2019
- Song, Xue-Yang; Wang, Chong; Vishwanath, Ashvin
- Nature Communications, Vol. 10, Issue 1
Mott Insulating States with Competing Orders in the Triangular Lattice Hubbard Model
journal, October 2021
- Wietek, Alexander; Rossi, Riccardo; Šimkovic, Fedor
- Physical Review X, Vol. 11, Issue 4
Thermodynamic Limit of Density Matrix Renormalization
journal, November 1995
- Östlund, Stellan; Rommer, Stefan
- Physical Review Letters, Vol. 75, Issue 19
Enhanced pairing correlations in the two-leg Hubbard ladder
journal, September 1997
- Noack, R. M.; Bulut, N.; Scalapino, D. J.
- Physical Review B, Vol. 56, Issue 12
Density matrix renormalization group study of superconductivity in the triangular lattice Hubbard model
journal, August 2019
- Venderley, Jordan; Kim, Eun-Ah
- Physical Review B, Vol. 100, Issue 6
Mott metal-insulator transition in the half-filled Hubbard model on the triangular lattice
journal, February 2001
- Capone, Massimo; Capriotti, Luca; Becca, Federico
- Physical Review B, Vol. 63, Issue 8
The Resonating Valence Bond State in La2CuO4 and Superconductivity
journal, March 1987
- Anderson, P. W.
- Science, Vol. 235, Issue 4793
Quantum phase diagram of the triangular-lattice antiferromagnet
journal, January 2015
- Koutroulakis, G.; Zhou, T.; Kamiya, Y.
- Physical Review B, Vol. 91, Issue 2
Superconductivity in the repulsive Hubbard model: An asymptotically exact weak-coupling solution
journal, June 2010
- Raghu, S.; Kivelson, S. A.; Scalapino, D. J.
- Physical Review B, Vol. 81, Issue 22
Phase diagram of the Hubbard model on the anisotropic triangular lattice
journal, June 2015
- Laubach, Manuel; Thomale, Ronny; Platt, Christian
- Physical Review B, Vol. 91, Issue 24
Exact sign structure of the t – J chain and the single hole ground state
journal, February 2016
- Zhu, Zheng; Wang, Qing-Rui; Sheng, D. N.
- Nuclear Physics B, Vol. 903
Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model
journal, July 2020
- Qin, Mingpu; Chung, Chia-Min; Shi, Hao
- Physical Review X, Vol. 10, Issue 3
Dirac Spin Liquid on the Spin- Triangular Heisenberg Antiferromagnet
journal, November 2019
- Hu, Shijie; Zhu, W.; Eggert, Sebastian
- Physical Review Letters, Vol. 123, Issue 20
Pairing versus phase coherence of doped holes in distinct quantum spin backgrounds
journal, March 2018
- Zhu, Zheng; Sheng, D. N.; Weng, Zheng-Yu
- Physical Review B, Vol. 97, Issue 11
Plaquette versus ordinary -wave pairing in the -Hubbard model on a width-4 cylinder
journal, July 2020
- Chung, Chia-Min; Qin, Mingpu; Zhang, Shiwei
- Physical Review B, Vol. 102, Issue 4
Gapless spin liquid and pair density wave of the Hubbard model on three-leg triangular cylinders
journal, December 2021
- Peng, Cheng; Jiang, Yi-Fan; Wang, Yao
- New Journal of Physics, Vol. 23, Issue 12
Gapless Quantum Spin Liquid in an Organic Spin-1/2 Triangular-Lattice
journal, April 2014
- Isono, Takayuki; Kamo, Hiromichi; Ueda, Akira
- Physical Review Letters, Vol. 112, Issue 17
Superconductivity in layers and the resonating valence bond mean-field theory of the triangular lattice model
journal, September 2003
- Kumar, Brijesh; Shastry, B. Sriram
- Physical Review B, Vol. 68, Issue 10
Correlated electronic phases in twisted bilayer transition metal dichalcogenides
journal, June 2020
- Wang, Lei; Shih, En-Min; Ghiotto, Augusto
- Nature Materials, Vol. 19, Issue 8
Spin-liquid-like state in pure and Mn-doped with a nearly triangular lattice
journal, July 2019
- Kim, M. G.; Winn, B.; Chi, S.
- Physical Review B, Vol. 100, Issue 2
Simple Variational Wave Functions for Two-Dimensional Heisenberg Spin-½ Antiferromagnets
journal, June 1988
- Huse, David A.; Elser, Veit
- Physical Review Letters, Vol. 60, Issue 24
Quantum spin chains and the Haldane gap
journal, May 1989
- Affleck, I.
- Journal of Physics: Condensed Matter, Vol. 1, Issue 19
Variational study of triangular lattice spin- model with ring exchanges and spin liquid state in
journal, July 2005
- Motrunich, Olexei I.
- Physical Review B, Vol. 72, Issue 4
Quasiparticle collapsing in an anisotropic ladder
journal, December 2015
- Zhu, Zheng; Weng, Zheng-Yu
- Physical Review B, Vol. 92, Issue 23
Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t ′
journal, September 2019
- Jiang, Hong-Chen; Devereaux, Thomas P.
- Science, Vol. 365, Issue 6460
Quantum Excitations in Quantum Spin Ice
journal, October 2011
- Ross, Kate A.; Savary, Lucile; Gaulin, Bruce D.
- Physical Review X, Vol. 1, Issue 2
From quantum matter to high-temperature superconductivity in copper oxides
journal, February 2015
- Keimer, B.; Kivelson, S. A.; Norman, M. R.
- Nature, Vol. 518, Issue 7538
Gapless quantum spin liquid ground state in the two-dimensional spin-1/2 triangular antiferromagnet YbMgGaO4
journal, November 2015
- Li, Yuesheng; Liao, Haijun; Zhang, Zhen
- Scientific Reports, Vol. 5, Issue 1
Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model
journal, September 2016
- Cheuk, L. W.; Nichols, M. A.; Lawrence, K. R.
- Science, Vol. 353, Issue 6305
A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice
journal, November 2009
- Bakr, Waseem S.; Gillen, Jonathon I.; Peng, Amy
- Nature, Vol. 462, Issue 7269
Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices
journal, March 2020
- Tang, Yanhao; Li, Lizhong; Li, Tingxin
- Nature, Vol. 579, Issue 7799
Single-atom-resolved fluorescence imaging of an atomic Mott insulator
journal, August 2010
- Sherson, Jacob F.; Weitenberg, Christof; Endres, Manuel
- Nature, Vol. 467, Issue 7311
Direct Determination of Exchange Parameters in and : High-Field Electron-Spin-Resonance Studies
journal, February 2014
- Zvyagin, S. A.; Kamenskyi, D.; Ozerov, M.
- Physical Review Letters, Vol. 112, Issue 7
Pressure-tuning the quantum spin Hamiltonian of the triangular lattice antiferromagnet Cs2CuCl4
journal, March 2019
- Zvyagin, S. A.; Graf, D.; Sakurai, T.
- Nature Communications, Vol. 10, Issue 1
Highly Mobile Gapless Excitations in a Two-Dimensional Candidate Quantum Spin Liquid
journal, June 2010
- Yamashita, M.; Nakata, N.; Senshu, Y.
- Science, Vol. 328, Issue 5983
Gapless spin liquid of an organic triangular compound evidenced by thermodynamic measurements
journal, April 2011
- Yamashita, Satoshi; Yamamoto, Takashi; Nakazawa, Yasuhiro
- Nature Communications, Vol. 2, Issue 1
Pair correlations in doped Hubbard ladders
journal, November 2015
- Dolfi, Michele; Bauer, Bela; Keller, Sebastian
- Physical Review B, Vol. 92, Issue 19
Correlated electrons in high-temperature superconductors
journal, July 1994
- Dagotto, Elbio
- Reviews of Modern Physics, Vol. 66, Issue 3
Spin-liquid state in an organic spin-1/2 system on a triangular lattice, EtMe 3 Sb[Pd(dmit) 2 ] 2
journal, March 2007
- Itou, T.; Oyamada, A.; Maegawa, S.
- Journal of Physics: Condensed Matter, Vol. 19, Issue 14
Spin Liquid State in the Triangular Lattice
journal, April 2011
- Zhou, H. D.; Choi, E. S.; Li, G.
- Physical Review Letters, Vol. 106, Issue 14
Coulomb enhancement of superconducting pair-pair correlations in a -filled model for
journal, May 2016
- De Silva, W. Wasanthi; Gomes, N.; Mazumdar, S.
- Physical Review B, Vol. 93, Issue 20
Quantum spin liquid in the spin- triangular antiferromagnet
journal, March 2008
- Itou, T.; Oyamada, A.; Maegawa, S.
- Physical Review B, Vol. 77, Issue 10
Hubbard Model on the Triangular Lattice: Spiral Order and Spin Liquid
journal, March 2008
- Sahebsara, Peyman; Sénéchal, David
- Physical Review Letters, Vol. 100, Issue 13
Variational Monte Carlo Studies of Pairing Symmetry for thet–JModel on a Triangular Lattice
journal, December 2004
- Watanabe, Tsutomu; Yokoyama, Hisatoshi; Tanaka, Yukio
- Journal of the Physical Society of Japan, Vol. 73, Issue 12
Coulomb-enhanced superconducting pair correlations and paired-electron liquid in the frustrated quarter-filled band
journal, April 2016
- Gomes, Niladri; De Silva, W. Wasanthi; Dutta, Tirthankar
- Physical Review B, Vol. 93, Issue 16
Mott-Hubbard metal-insulator transition in nonbipartite lattices
journal, February 1990
- Krishnamurthy, H.; Jayaprakash, C.; Sarker, Sanjoy
- Physical Review Letters, Vol. 64, Issue 8
Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers
journal, February 2019
- Wu, Fengcheng; Lovorn, Timothy; Tutuc, Emanuel
- Physical Review Letters, Vol. 122, Issue 8
Continuous Mott transition between a metal and a quantum spin liquid
journal, June 2015
- Mishmash, Ryan V.; González, Iván; Melko, Roger G.
- Physical Review B, Vol. 91, Issue 23
Hubbard ladders at small revisited
journal, September 2020
- Gannot, Yuval; Jiang, Yi-Fan; Kivelson, Steven A.
- Physical Review B, Vol. 102, Issue 11
Spinon Fermi Surface in a Cluster Mott Insulator Model on a Triangular Lattice and Possible Application to
journal, July 2018
- He, Wen-Yu; Xu, Xiao Yan; Chen, Gang
- Physical Review Letters, Vol. 121, Issue 4
Predominant magnetic states in the Hubbard model on anisotropic triangular lattices
journal, June 2008
- Watanabe, T.; Yokoyama, H.; Tanaka, Y.
- Physical Review B, Vol. 77, Issue 21
Exact Diagonalization Study of Mott Transition in the Hubbard Model on an Anisotropic Triangular Lattice
journal, July 2007
- Koretsune, Takashi; Motome, Yukitoshi; Furusaki, Akira
- Journal of the Physical Society of Japan, Vol. 76, Issue 7
Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006
- Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang
- Reviews of Modern Physics, Vol. 78, Issue 1
Quantum Phase Transitions in the Hubbard Model on a Triangular Lattice
journal, July 2009
- Yoshioka, Takuya; Koga, Akihisa; Kawakami, Norio
- Physical Review Letters, Vol. 103, Issue 3
Thermodynamics of a Bad Metal–Mott Insulator Transition in the Presence of Frustration
journal, May 2013
- Kokalj, J.; McKenzie, Ross H.
- Physical Review Letters, Vol. 110, Issue 20
Absence of Superconductivity in the Half-Filled Band Hubbard Model on the Anisotropic Triangular Lattice
journal, October 2008
- Clay, R. T.; Li, H.; Mazumdar, S.
- Physical Review Letters, Vol. 101, Issue 16
Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model
journal, September 2016
- Parsons, M. F.; Mazurenko, A.; Chiu, C. S.
- Science, Vol. 353, Issue 6305
Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice
journal, September 2003
- Shimizu, Y.; Miyagawa, K.; Kanoda, K.
- Physical Review Letters, Vol. 91, Issue 10
Gapless spin-liquid state in the structurally disorder-free triangular antiferromagnet
journal, October 2019
- Ding, Lei; Manuel, Pascal; Bachus, Sebastian
- Physical Review B, Vol. 100, Issue 14
Doping the chiral spin liquid: Topological superconductor or chiral metal
journal, April 2021
- Song, Xue-Yang; Vishwanath, Ashvin; Zhang, Ya-Hui
- Physical Review B, Vol. 103, Issue 16