Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

Ding, Jixun K.; Yang, Luhang; Wang, Wen O.; Zhu, Ziyan; Peng, Cheng; Mai, Peizhi; Huang, Edwin W.; Moritz, Brian; Phillips, Philip W.; Feldman, Benjamin E.; Devereaux, Thomas P.

doi:10.1103/physrevx.14.041025

Title: Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

Journal Article · 25 October 2024 · Physical Review. X

DOI: https://doi.org/10.1103/physrevx.14.041025 · OSTI ID:2440438

^[1];

^[2];

^[3];

^[4]; Peng, Cheng ^[4];

^[5]; Huang, Edwin W. ^[6];

^[4]; Phillips, Philip W. ^[5];

^[3];

^[3]

SLAC National Accelerator Laboratory; Stanford University; SLAC National Accelerator Laboratory
SLAC National Accelerator Laboratory; Northeastern University
SLAC National Accelerator Laboratory; Stanford University
SLAC National Accelerator Laboratory
University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign; University of Notre Dame; University of Notre Dame

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν≤1, bounded below by filling factor ν=1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν=1 and ν=3. The phases near ν=1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: SLAC National Accelerator Laboratory

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 2440438

Journal Information:: Physical Review. X, Journal Name: Physical Review. X Journal Issue: 4 Vol. 14; ISSN 2160-3308

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (89)

A Result Not Dependent on Rationality for Bloch Electrons in a Magnetic Field Wannier, G. H. Physica Status Solidi (b), Vol. 88, Issue 2 https://doi.org/10.1002/pssb.2220880243	journal	August 1978
Fractional quantum Hall physics in topological flat bands Parameswaran, Siddharth A.; Roy, Rahul; Sondhi, Shivaji L. Comptes Rendus Physique, Vol. 14, Issue 9-10 https://doi.org/10.1016/j.crhy.2013.04.003	journal	November 2013
Fractional quantum Hall effect in the absence of Landau levels Sheng, D. N.; Gu, Zheng-Cheng; Sun, Kai Nature Communications, Vol. 2, Issue 1 https://doi.org/10.1038/ncomms1380	journal	July 2011
Baby skyrmions in Chern ferromagnets and topological mechanism for spin-polaron formation in twisted bilayer graphene Khalaf, Eslam; Vishwanath, Ashvin Nature Communications, Vol. 13, Issue 1 https://doi.org/10.1038/s41467-022-33673-3	journal	October 2022
Spin skyrmion gaps as signatures of strong-coupling insulators in magic-angle twisted bilayer graphene Yu, Jiachen; Foutty, Benjamin A.; Kwan, Yves H. Nature Communications, Vol. 14, Issue 1 https://doi.org/10.1038/s41467-023-42275-6	journal	October 2023
Pressure-induced charge orders and their postulated coupling to magnetism in hexagonal multiferroic LuFe2O4 Liu, Fengliang; Hao, Yiqing; Ni, Jinyang npj Quantum Materials, Vol. 8, Issue 1 https://doi.org/10.1038/s41535-022-00522-x	journal	January 2023
Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene Wu, Shuang; Zhang, Zhenyuan; Watanabe, K. Nature Materials, Vol. 20, Issue 4 https://doi.org/10.1038/s41563-020-00911-2	journal	February 2021
Semiconductor moiré materials Mak, Kin Fai; Shan, Jie Nature Nanotechnology, Vol. 17, Issue 7 https://doi.org/10.1038/s41565-022-01165-6	journal	July 2022
A tunable bilayer Hubbard model in twisted WSe2 Xu, Yang; Kang, Kaifei; Watanabe, Kenji Nature Nanotechnology, Vol. 17, Issue 9 https://doi.org/10.1038/s41565-022-01180-7	journal	August 2022
Evidence of frustrated magnetic interactions in a Wigner–Mott insulator Tang, Yanhao; Su, Kaixiang; Li, Lizhong Nature Nanotechnology, Vol. 18, Issue 3 https://doi.org/10.1038/s41565-022-01309-8	journal	January 2023
Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene Saito, Yu; Ge, Jingyuan; Rademaker, Louk Nature Physics, Vol. 17, Issue 4 https://doi.org/10.1038/s41567-020-01129-4	journal	January 2021
Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene Das, Ipsita; Lu, Xiaobo; Herzog-Arbeitman, Jonah Nature Physics, Vol. 17, Issue 6 https://doi.org/10.1038/s41567-021-01186-3	journal	March 2021
Correlated Hofstadter spectrum and flavour phase diagram in magic-angle twisted bilayer graphene Yu, Jiachen; Foutty, Benjamin A.; Han, Zhaoyu Nature Physics, Vol. 18, Issue 7 https://doi.org/10.1038/s41567-022-01589-w	journal	April 2022
Hofstadter states and re-entrant charge order in a semiconductor moiré lattice Kometter, Carlos R.; Yu, Jiachen; Devakul, Trithep Nature Physics, Vol. 19, Issue 12 https://doi.org/10.1038/s41567-023-02195-0	journal	September 2023
Correlation-driven topological phases in magic-angle twisted bilayer graphene Choi, Youngjoon; Kim, Hyunjin; Peng, Yang Nature, Vol. 589, Issue 7843 https://doi.org/10.1038/s41586-020-03159-7	journal	January 2021
Evidence of flat bands and correlated states in buckled graphene superlattices Mao, Jinhai; Milovanović, Slaviša P.; Anđelković, Miša Nature, Vol. 584, Issue 7820 https://doi.org/10.1038/s41586-020-2567-3	journal	August 2020
Strongly correlated Chern insulators in magic-angle twisted bilayer graphene Nuckolls, Kevin P.; Oh, Myungchul; Wong, Dillon Nature, Vol. 588, Issue 7839 https://doi.org/10.1038/s41586-020-3028-8	journal	December 2020
Flavour Hund’s coupling, Chern gaps and charge diffusivity in moiré graphene Park, Jeong Min; Cao, Yuan; Watanabe, Kenji Nature, Vol. 592, Issue 7852 https://doi.org/10.1038/s41586-021-03366-w	journal	March 2021
Frustration- and doping-induced magnetism in a Fermi–Hubbard simulator Xu, Muqing; Kendrick, Lev Haldar; Kale, Anant Nature, Vol. 620, Issue 7976 https://doi.org/10.1038/s41586-023-06280-5	journal	August 2023
Thermodynamics of correlated electrons in a magnetic field Ding, Jixun K.; Wang, Wen O.; Moritz, Brian Communications Physics, Vol. 5, Issue 1 https://doi.org/10.1038/s42005-022-00968-2	journal	August 2022
Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model Palm, F. A.; Kurttutan, M.; Bohrdt, A. New Journal of Physics, Vol. 25, Issue 2 https://doi.org/10.1088/1367-2630/acb963	journal	February 2023
Site-Resolved Imaging of Ultracold Fermions in a Triangular-Lattice Quantum Gas Microscope Yang, Jin; Liu, Liyu; Mongkolkiattichai, Jirayu PRX Quantum, Vol. 2, Issue 2 https://doi.org/10.1103/PRXQuantum.2.020344	journal	June 2021
Magnetic Translation Group Zak, J. Physical Review, Vol. 134, Issue 6A https://doi.org/10.1103/PhysRev.134.A1602	journal	June 1964
Site-resolved observables in the doped spin-imbalanced triangular Hubbard model Garwood, Davis; Mongkolkiattichai, Jirayu; Liu, Liyu Physical Review A, Vol. 106, Issue 1 https://doi.org/10.1103/PhysRevA.106.013310	journal	July 2022
Quantum gas microscopy of fermionic triangular-lattice Mott insulators Mongkolkiattichai, Jirayu; Liu, Liyu; Garwood, Davis Physical Review A, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevA.108.L061301	journal	December 2023
Symmetry breaking and skyrmionic transport in twisted bilayer graphene Chatterjee, Shubhayu; Bultinck, Nick; Zaletel, Michael P. Physical Review B, Vol. 101, Issue 16 https://doi.org/10.1103/PhysRevB.101.165141	journal	April 2020
Quantum geometry and stability of moiré flatband ferromagnetism Wu, Fengcheng; Das Sarma, S. Physical Review B, Vol. 102, Issue 16 https://doi.org/10.1103/PhysRevB.102.165118	journal	October 2020
Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model Andrews, Bartholomew; Neupert, Titus; Möller, Gunnar Physical Review B, Vol. 104, Issue 12 https://doi.org/10.1103/PhysRevB.104.125107	journal	September 2021
Fractional Chern insulators with a non-Landau level continuum limit Bauer, David; Talkington, Spenser; Harper, Fenner Physical Review B, Vol. 105, Issue 4 https://doi.org/10.1103/PhysRevB.105.045144	journal	January 2022
Trions in twisted bilayer graphene Schindler, Frank; Vafek, Oskar; Bernevig, B. Andrei Physical Review B, Vol. 105, Issue 15 https://doi.org/10.1103/PhysRevB.105.155135	journal	April 2022
Doped Mott insulators in the triangular-lattice Hubbard model Zhu, Zheng; Sheng, D. N.; Vishwanath, Ashvin Physical Review B, Vol. 105, Issue 20 https://doi.org/10.1103/PhysRevB.105.205110	journal	May 2022
Skyrmion superconductivity: DMRG evidence for a topological route to superconductivity Chatterjee, Shubhayu; Ippoliti, Matteo; Zaletel, Michael P. Physical Review B, Vol. 106, Issue 3 https://doi.org/10.1103/PhysRevB.106.035421	journal	July 2022
Vortexability: A unifying criterion for ideal fractional Chern insulators Ledwith, Patrick J.; Vishwanath, Ashvin; Parker, Daniel E. Physical Review B, Vol. 108, Issue 20 https://doi.org/10.1103/PhysRevB.108.205144	journal	November 2023
Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields Hofstadter, Douglas R. Physical Review B, Vol. 14, Issue 6 https://doi.org/10.1103/PhysRevB.14.2239	journal	September 1976
Magneto-roton theory of collective excitations in the fractional quantum Hall effect Girvin, S. M.; MacDonald, A. H.; Platzman, P. M. Physical Review B, Vol. 33, Issue 4 https://doi.org/10.1103/PhysRevB.33.2481	journal	February 1986
Numerical study of the two-dimensional Hubbard model White, S. R.; Scalapino, D. J.; Sugar, R. L. Physical Review B, Vol. 40, Issue 1 https://doi.org/10.1103/PhysRevB.40.506	journal	July 1989
Sign problem in the numerical simulation of many-electron systems Loh, E. Y.; Gubernatis, J. E.; Scalettar, R. T. Physical Review B, Vol. 41, Issue 13 https://doi.org/10.1103/PhysRevB.41.9301	journal	May 1990
Wave functions and other properties of spin-reversed quasiparticles at ν=1/ m Landau-level occupation Rezayi, E. H. Physical Review B, Vol. 43, Issue 7 https://doi.org/10.1103/PhysRevB.43.5944	journal	March 1991
Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies Sondhi, S. L.; Karlhede, A.; Kivelson, S. A. Physical Review B, Vol. 47, Issue 24 https://doi.org/10.1103/PhysRevB.47.16419	journal	June 1993
Density-matrix algorithms for quantum renormalization groups White, Steven R. Physical Review B, Vol. 48, Issue 14 https://doi.org/10.1103/PhysRevB.48.10345	journal	October 1993
Skyrmions in higher Landau levels Wu, X. -G.; Sondhi, S. L. Physical Review B, Vol. 51, Issue 20 https://doi.org/10.1103/PhysRevB.51.14725	journal	May 1995
Hartree-Fock theory of Skyrmions in quantum Hall ferromagnets Fertig, H. A.; Brey, Luis; Côté, R. Physical Review B, Vol. 55, Issue 16 https://doi.org/10.1103/PhysRevB.55.10671	journal	April 1997
Critical comparison of classical field theory and microscopic wave functions for skyrmions in quantum Hall ferromagnets Abolfath, M.; Palacios, J. J.; Fertig, H. A. Physical Review B, Vol. 56, Issue 11 https://doi.org/10.1103/PhysRevB.56.6795	journal	September 1997
Skyrmion physics beyond the lowest Landau-level approximation Melik-Alaverdian, V.; Bonesteel, N. E.; Ortiz, G. Physical Review B, Vol. 60, Issue 12 https://doi.org/10.1103/PhysRevB.60.R8501	journal	September 1999
Landau-level mixing and skyrmion stability in quantum Hall ferromagnets Mihalek, I.; Fertig, H. A. Physical Review B, Vol. 62, Issue 20 https://doi.org/10.1103/PhysRevB.62.13573	journal	November 2000
Depleted Kondo lattices: Quantum Monte Carlo and mean-field calculations Assaad, F. F. Physical Review B, Vol. 65, Issue 11 https://doi.org/10.1103/PhysRevB.65.115104	journal	February 2002
Spin excitation spectra of integral and fractional quantum Hall systems Wójs, Arkadiusz; Quinn, John J. Physical Review B, Vol. 66, Issue 4 https://doi.org/10.1103/PhysRevB.66.045323	journal	July 2002
Fractional Chern insulators and the W ∞ algebra Parameswaran, S. A.; Roy, R.; Sondhi, S. L. Physical Review B, Vol. 85, Issue 24 https://doi.org/10.1103/PhysRevB.85.241308	journal	June 2012
Continuous transitions between composite Fermi liquid and Landau Fermi liquid: A route to fractionalized Mott insulators Barkeshli, Maissam; McGreevy, John Physical Review B, Vol. 86, Issue 7 https://doi.org/10.1103/PhysRevB.86.075136	journal	August 2012
Band geometry of fractional topological insulators Roy, Rahul Physical Review B, Vol. 90, Issue 16 https://doi.org/10.1103/PhysRevB.90.165139	journal	October 2014
NMR probing of spin and charge order near odd-integer filling in the second Landau level Rhone, T. D.; Tiemann, L.; Muraki, K. Physical Review B, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevB.92.041301	journal	July 2015
Geometry dependence of the sign problem in quantum Monte Carlo simulations Iglovikov, V. I.; Khatami, E.; Scalettar, R. T. Physical Review B, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevB.92.045110	journal	July 2015
Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model Bauer, David; Jackson, T. S.; Roy, Rahul Physical Review B, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevB.93.235133	journal	June 2016
Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number \|C\|>1 Andrews, Bartholomew; Möller, Gunnar Physical Review B, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevB.97.035159	journal	January 2018
Nearly flat Chern bands in moiré superlattices Zhang, Ya-Hui; Mao, Dan; Cao, Yuan Physical Review B, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevB.99.075127	journal	February 2019
Exact Parent Hamiltonian for the Quantum Hall States in a Lattice Kapit, Eliot; Mueller, Erich Physical Review Letters, Vol. 105, Issue 21 https://doi.org/10.1103/PhysRevLett.105.215303	journal	November 2010
Generic Wave-Function Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators Qi, Xiao-Liang Physical Review Letters, Vol. 107, Issue 12 https://doi.org/10.1103/PhysRevLett.107.126803	journal	September 2011
Multiple- q States and the Skyrmion Lattice of the Triangular-Lattice Heisenberg Antiferromagnet under Magnetic Fields Okubo, Tsuyoshi; Chung, Sungki; Kawamura, Hikaru Physical Review Letters, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevLett.108.017206	journal	January 2012
Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions Cocks, Daniel; Orth, Peter P.; Rachel, Stephan Physical Review Letters, Vol. 109, Issue 20 https://doi.org/10.1103/PhysRevLett.109.205303	journal	November 2012
Adiabatic Continuation of Fractional Chern Insulators to Fractional Quantum Hall States Scaffidi, Thomas; Möller, Gunnar Physical Review Letters, Vol. 109, Issue 24 https://doi.org/10.1103/PhysRevLett.109.246805	journal	December 2012
Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators Claassen, Martin; Lee, Ching Hua; Thomale, Ronny Physical Review Letters, Vol. 114, Issue 23 https://doi.org/10.1103/PhysRevLett.114.236802	journal	June 2015
Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number Möller, Gunnar; Cooper, Nigel R. Physical Review Letters, Vol. 115, Issue 12 https://doi.org/10.1103/PhysRevLett.115.126401	journal	September 2015
Competing Orders in a Nearly Antiferromagnetic Metal Schattner, Yoni; Gerlach, Max H.; Trebst, Simon Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.097002	journal	August 2016
Hubbard Model Physics in Transition Metal Dichalcogenide Moiré Bands Wu, Fengcheng; Lovorn, Timothy; Tutuc, Emanuel Physical Review Letters, Vol. 121, Issue 2 https://doi.org/10.1103/PhysRevLett.121.026402	journal	July 2018
Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers Wu, Fengcheng; Lovorn, Timothy; Tutuc, Emanuel Physical Review Letters, Vol. 122, Issue 8 https://doi.org/10.1103/PhysRevLett.122.086402	journal	February 2019
Competing Zero-Field Chern Insulators in Superconducting Twisted Bilayer Graphene Stepanov, Petr; Xie, Ming; Taniguchi, Takashi Physical Review Letters, Vol. 127, Issue 19 https://doi.org/10.1103/PhysRevLett.127.197701	journal	November 2021
Exact Landau Level Description of Geometry and Interaction in a Flatband Wang, Jie; Cano, Jennifer; Millis, Andrew J. Physical Review Letters, Vol. 127, Issue 24 https://doi.org/10.1103/PhysRevLett.127.246403	journal	December 2021
SU(4) Chiral Spin Liquid, Exciton Supersolid, and Electric Detection in Moiré Bilayers Zhang, Ya-Hui; Sheng, D. N.; Vishwanath, Ashvin Physical Review Letters, Vol. 127, Issue 24 https://doi.org/10.1103/PhysRevLett.127.247701	journal	December 2021
Nonlocal Interactions in Moiré Hubbard Systems Morales-Durán, Nicolás; Hu, Nai Chao; Potasz, Pawel Physical Review Letters, Vol. 128, Issue 21 https://doi.org/10.1103/PhysRevLett.128.217202	journal	May 2022
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
Optically Pumped NMR Evidence for Finite-Size Skyrmions in GaAs Quantum Wells near Landau Level Filling ν = 1 Barrett, S. E.; Dabbagh, G.; Pfeiffer, L. N. Physical Review Letters, Vol. 74, Issue 25 https://doi.org/10.1103/PhysRevLett.74.5112	journal	June 1995
Thermodynamic Limit of Density Matrix Renormalization Östlund, Stellan; Rommer, Stefan Physical Review Letters, Vol. 75, Issue 19 https://doi.org/10.1103/PhysRevLett.75.3537	journal	November 1995
Evidence for Skyrmions and Single Spin Flips in the Integer Quantized Hall Effect Schmeller, A.; Eisenstein, J. P.; Pfeiffer, L. N. Physical Review Letters, Vol. 75, Issue 23 https://doi.org/10.1103/PhysRevLett.75.4290	journal	December 1995
Skyrmions without Sigma Models in Quantum Hall Ferromagnets MacDonald, A. H.; Fertig, H. A.; Brey, Luis Physical Review Letters, Vol. 76, Issue 12 https://doi.org/10.1103/PhysRevLett.76.2153	journal	March 1996
Evidence of Skyrmion Excitations about ν = 1 in n -Modulation-Doped Single Quantum Wells by Interband Optical Transmission Aifer, E. H.; Goldberg, B. B.; Broido, D. A. Physical Review Letters, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevLett.76.680	journal	January 1996
Chern bands of twisted bilayer graphene: Fractional Chern insulators and spin phase transition Repellin, Cécile; Senthil, T. Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023238	journal	May 2020
Fractional Chern Insulator Regnault, N.; Bernevig, B. Andrei Physical Review X, Vol. 1, Issue 2 https://doi.org/10.1103/PhysRevX.1.021014	journal	December 2011
Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study Szasz, Aaron; Motruk, Johannes; Zaletel, Michael P. Physical Review X, Vol. 10, Issue 2 https://doi.org/10.1103/PhysRevX.10.021042	journal	May 2020
Skyrmions in Twisted Bilayer Graphene: Stability, Pairing, and Crystallization Kwan, Yves H.; Wagner, Glenn; Bultinck, Nick Physical Review X, Vol. 12, Issue 3 https://doi.org/10.1103/PhysRevX.12.031020	journal	July 2022
Chiral Pseudospin Liquids in Moiré Heterostructures Kuhlenkamp, Clemens; Kadow, Wilhelm; Imamoğlu, Ataç Physical Review X, Vol. 14, Issue 2 https://doi.org/10.1103/PhysRevX.14.021013	journal	April 2024
Berry phase effects on electronic properties Xiao, Di; Chang, Ming-Che; Niu, Qian Reviews of Modern Physics, Vol. 82, Issue 3 https://doi.org/10.1103/RevModPhys.82.1959	journal	July 2010
Charged skyrmions and topological origin of superconductivity in magic-angle graphene Khalaf, Eslam; Chatterjee, Shubhayu; Bultinck, Nick Science Advances, Vol. 7, Issue 19 https://doi.org/10.1126/sciadv.abf5299	journal	May 2021
Strain-Induced Pseudo-Magnetic Fields Greater Than 300 Tesla in Graphene Nanobubbles Levy, N.; Burke, S. A.; Meaker, K. L. Science, Vol. 329, Issue 5991 https://doi.org/10.1126/science.1191700	journal	July 2010
Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure Hunt, B.; Sanchez-Yamagishi, J. D.; Young, A. F. Science, Vol. 340, Issue 6139 https://doi.org/10.1126/science.1237240	journal	May 2013
Observation of chiral edge states with neutral fermions in synthetic Hall ribbons Mancini, M.; Pagano, G.; Cappellini, G. Science, Vol. 349, Issue 6255 https://doi.org/10.1126/science.aaa8736	journal	September 2015
Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains Dukelsky, J.; Martín-Delgado, M. A.; Nishino, T. Europhysics Letters (EPL), Vol. 43, Issue 4 https://doi.org/10.1209/epl/i1998-00381-x	journal	August 1998
The ITensor Software Library for Tensor Network Calculations Fishman, Matthew; White, Steven; Stoudenmire, Edwin SciPost Physics Codebases https://doi.org/10.21468/SciPostPhysCodeb.4	journal	August 2022
Codebase release 0.3 for ITensor Fishman, Matthew; White, Steven; Stoudenmire, Edwin SciPost Physics Codebases https://doi.org/10.21468/SciPostPhysCodeb.4-r0.3	journal	August 2022
Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model Zenodo https://doi.org/10.5281/zenodo.13845680	dataset	January 2024

Title: Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

References (89)

Similar Records

Related Subjects

Title: Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

Citation Formats

References (89)

Similar Records

Related Subjects