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Bohrdt A, Wang Y, Koepsell J, Kánasz-Nagy M, Demler E, Grusdt F. Dominant Fifth-Order Correlations in Doped Quantum Antiferromagnets. PHYSICAL REVIEW LETTERS 2021; 126:026401. [PMID: 33512175 DOI: 10.1103/physrevlett.126.026401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 12/11/2020] [Indexed: 06/12/2023]
Abstract
Traditionally, one- and two-point correlation functions are used to characterize many-body systems. In strongly correlated quantum materials, such as the doped 2D Fermi-Hubbard system, these may no longer be sufficient, because higher-order correlations are crucial to understanding the character of the many-body system and can be numerically dominant. Experimentally, such higher-order correlations have recently become accessible in ultracold atom systems. Here, we reveal strong non-Gaussian correlations in doped quantum antiferromagnets and show that higher-order correlations dominate over lower-order terms. We study a single mobile hole in the t-J model using the density matrix renormalization group and reveal genuine fifth-order correlations which are directly related to the mobility of the dopant. We contrast our results to predictions using models based on doped quantum spin liquids which feature significantly reduced higher-order correlations. Our predictions can be tested at the lowest currently accessible temperatures in quantum simulators of the 2D Fermi-Hubbard model. Finally, we propose to experimentally study the same fifth-order spin-charge correlations as a function of doping. This will help to reveal the microscopic nature of charge carriers in the most debated regime of the Hubbard model, relevant for understanding high-T_{c} superconductivity.
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Affiliation(s)
- A Bohrdt
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
| | - Y Wang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
| | - J Koepsell
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - M Kánasz-Nagy
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - E Demler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - F Grusdt
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstrasse 37, München D-80333, Germany
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Chiu CS, Ji G, Bohrdt A, Xu M, Knap M, Demler E, Grusdt F, Greiner M, Greif D. String patterns in the doped Hubbard model. Science 2020; 365:251-256. [PMID: 31320533 DOI: 10.1126/science.aav3587] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Accepted: 06/05/2019] [Indexed: 11/02/2022]
Abstract
Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly correlated electrons in solids. In this work, we realize the Hubbard Hamiltonian and search for specific patterns within the individual images of many realizations of strongly correlated ultracold fermions in an optical lattice. Upon doping a cold-atom antiferromagnet, we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables. Our results demonstrate the potential for pattern recognition to provide key insights into cold-atom quantum many-body systems.
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Affiliation(s)
- Christie S Chiu
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Geoffrey Ji
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Annabelle Bohrdt
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.,Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Muqing Xu
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Michael Knap
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Eugene Demler
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Fabian Grusdt
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Markus Greiner
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA.
| | - Daniel Greif
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
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Piazza BD, Mourigal M, Christensen NB, Nilsen GJ, Tregenna-Piggott P, Perring TG, Enderle M, McMorrow DF, Ivanov DA, Rønnow HM. Fractional excitations in the square lattice quantum antiferromagnet. NATURE PHYSICS 2015; 11:62-68. [PMID: 25729400 PMCID: PMC4340518 DOI: 10.1038/nphys3172] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2014] [Accepted: 10/29/2014] [Indexed: 05/30/2023]
Abstract
Quantum magnets have occupied the fertile ground between many-body theory and low-temperature experiments on real materials since the early days of quantum mechanics. However, our understanding of even deceptively simple systems of interacting spins-1/2 is far from complete. The quantum square-lattice Heisenberg antiferromagnet (QSLHAF), for example, exhibits a striking anomaly of hitherto unknown origin in its magnetic excitation spectrum. This quantum effect manifests itself for excitations propagating with the specific wave vector (π, 0). We use polarized neutron spectroscopy to fully characterize the magnetic fluctuations in the metal-organic compound CFTD, a known realization of the QSLHAF model. Our experiments reveal an isotropic excitation continuum at the anomaly, which we analyse theoretically using Gutzwiller-projected trial wavefunctions. The excitation continuum is accounted for by the existence of spatially-extended pairs of fractional S=1/2 quasiparticles, 2D analogues of 1D spinons. Away from the anomalous wave vector, these fractional excitations are bound and form conventional magnons. Our results establish the existence of fractional quasiparticles in the high-energy spectrum of a quasi-two-dimensional antiferromagnet, even in the absence of frustration.
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Affiliation(s)
- B Dalla Piazza
- Laboratory for Quantum Magnetism, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Switzerland
| | - M Mourigal
- Laboratory for Quantum Magnetism, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Switzerland ; Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France ; Institute for Quantum Matter and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA
| | - N B Christensen
- Department of Physics, Technical University of Denmark (DTU), DK-2800 Kgs. Lyngby, Denmark ; Laboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - G J Nilsen
- Laboratory for Quantum Magnetism, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Switzerland ; Department of Chemistry, University of Edinburgh, Edinburgh, EH9 3JJ, United Kingdom
| | - P Tregenna-Piggott
- Laboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - T G Perring
- ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 OQX, United Kingdom
| | - M Enderle
- Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France
| | - D F McMorrow
- London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1H 0AH, United Kingdom
| | - D A Ivanov
- Institute for Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland ; Institute for Theoretical Physics, University of Zürich, CH-8057 Zürich, Switzerland
| | - H M Rønnow
- Laboratory for Quantum Magnetism, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Switzerland ; RIKEN Centre for Emergent Matter Science (CEMS), Wako 351-0198, Japan
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Shih CT, Lee TK, Eder R, Mou CY, Chen YC. Enhancement of pairing correlation by t' in the two-dimensional extended t-J model. PHYSICAL REVIEW LETTERS 2004; 92:227002. [PMID: 15245252 DOI: 10.1103/physrevlett.92.227002] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2003] [Indexed: 05/24/2023]
Abstract
We investigate the effects of the next-nearest-neighbor (t') and the third-nearest-neighbor (t") hopping terms on superconductivity correlation in the 2D hole-doped extended t-J model based on the variational Monte Carlo, mean-field calculation and exact diagonalization method. Despite the diversity of the methods employed, the results all point to a consistent conclusion: While the d-wave superconductivity correlation is slightly suppressed by t' and t" in underdoped regions, it is greatly enhanced in the optimal and overdoped regions. The optimal Tc is a result of the balance of these two opposite trends.
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Affiliation(s)
- C T Shih
- Department of Physics, Tunghai University, Taichung, Taiwan
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Lee WC, Lee TK, Ho CM, Leung PW. Low-energy spectra in t-J-type models at low doping levels. PHYSICAL REVIEW LETTERS 2003; 91:057001. [PMID: 12906623 DOI: 10.1103/physrevlett.91.057001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2003] [Indexed: 05/24/2023]
Abstract
Based on a variational approach, we propose that there are two kinds of low-energy states in the t-J-type models at low doping. In a quasiparticle state an unpaired spin bound to a hole with a well-defined momentum can be excited with spin waves. The resulting state shows a suppression of antiferromagnetic order around the hole with the profile of a spin bag. These spin-bag states with spin and charge or hole separated form a continuum of low-energy excitations. Very different properties predicted by these two kinds of states explain a number of anomalous results observed in the exact diagonalization studies on small clusters up to 32 sites.
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Affiliation(s)
- Wei-Cheng Lee
- Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan 11529
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Lee TK, Ho CM, Nagaosa N. Theory for slightly doped antiferromagnetic mott insulators. PHYSICAL REVIEW LETTERS 2003; 90:067001. [PMID: 12633317 DOI: 10.1103/physrevlett.90.067001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2002] [Indexed: 05/24/2023]
Abstract
New trial wave functions, constructed explicitly from the unique Mott insulating state with antiferromagnetic order, are proposed to describe the ground state of a Mott insulator slightly doped with holes or electrons. A rigid band is observed as charged quasiparticles with well-defined momenta being realized in these states. These states have much less superconducting correlations than previously studied ones. Small Fermi patches obtained are consistent with recent experiments on high T(c) cuprates doped lightly with holes or electrons.
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Affiliation(s)
- T K Lee
- Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan 11529
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Feng S. Jordan-Wigner approach to the spin excitation spectrum in the Heisenberg antiferromagnet. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:11671-11677. [PMID: 9982791 DOI: 10.1103/physrevb.53.11671] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chen YC, Lee TK. t-J model studied by the power Lanczos method. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:6723-6726. [PMID: 9977212 DOI: 10.1103/physrevb.51.6723] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Feng S, Su ZB, Yu L. Fermion-spin transformation to implement the charge-spin separation. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:2368-2384. [PMID: 10011071 DOI: 10.1103/physrevb.49.2368] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Liu Y, Dong J, Gong C, Chen T. Variational Monte Carlo study of the spiral state in the Hubbard model. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:1306-1309. [PMID: 10008000 DOI: 10.1103/physrevb.48.1306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Feng S, Wu JB, Su ZB, Yu L. Slave-particle studies of the electron-momentum distribution in the low-dimensional t-J model. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:15192-15200. [PMID: 10005893 DOI: 10.1103/physrevb.47.15192] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Giamarchi T, Lhuillier C. Dispersion relation of a single hole in the t-J model determined by a variational Monte Carlo method. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:2775-2779. [PMID: 10006335 DOI: 10.1103/physrevb.47.2775] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Khaliullin G, Horsch P. Doping dependence of long-range magnetic order in the t-J model. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:463-469. [PMID: 10004465 DOI: 10.1103/physrevb.47.463] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Maska M. Metallic and magnetic properties of the t-J model: One-site approximation. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:13088-13091. [PMID: 10001381 DOI: 10.1103/physrevb.45.13088] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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16
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Johnson MD, Gros C. Geometry-controlled conserving approximations for the t-J model. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:11207-11239. [PMID: 9996860 DOI: 10.1103/physrevb.43.11207] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hsu TC, Marston JB, Affleck I. Two observable features of the staggered-flux phase at nonzero doping. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:2866-2877. [PMID: 9997586 DOI: 10.1103/physrevb.43.2866] [Citation(s) in RCA: 50] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lee TK, Chang LN. Energies of the staggered flux phase: A numerical study. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:8720-8723. [PMID: 9995073 DOI: 10.1103/physrevb.42.8720] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Gros C. Criterion for a good variational wave function. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:6835-6838. [PMID: 9994799 DOI: 10.1103/physrevb.42.6835] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Chen GJ, Joynt R, Zhang FC, Gros C. Phases of the t-J model from variational Monte Carlo studies: Occurrence of time-reversal symmetry breaking. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:2662-2664. [PMID: 9995744 DOI: 10.1103/physrevb.42.2662] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hsu TC. Spin waves in the flux-phase description of the S=1/2 Heisenberg antiferromagnet. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:11379-11387. [PMID: 9993558 DOI: 10.1103/physrevb.41.11379] [Citation(s) in RCA: 74] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Lee TK, Feng S. Resonating-valence-bond wave function for the two-dimensional Heisenberg model on a triangular lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:11110-11113. [PMID: 9993529 DOI: 10.1103/physrevb.41.11110] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Zhang FC. Superconducting instability of staggered-flux phase in the t-J model. PHYSICAL REVIEW LETTERS 1990; 64:974-977. [PMID: 10042128 DOI: 10.1103/physrevlett.64.974] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Fazekas P, Menge B, M�ller-Hartmann E. Ground state phase diagram of the infinite dimensional Hubbard model: A variational study. ACTA ACUST UNITED AC 1990. [DOI: 10.1007/bf01317359] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Chen H, Su Z, Yu L. Antiferromagnetism and superconductivity in a two-dimensional Heisenberg model: Further studies on possible coexistence. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:267-272. [PMID: 9992764 DOI: 10.1103/physrevb.41.267] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kobayashi K, Iguchi K. Pairing mechanism in the CuO2 system based on a variational Monte Carlo study with magnetically frustrated wave function. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:7073-7079. [PMID: 9991091 DOI: 10.1103/physrevb.40.7073] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Miyazaki M, Inoue J, Maekawa S. Stability of resonating-valence-bond state in the Hubbard model near half filling. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:6611-6616. [PMID: 9991031 DOI: 10.1103/physrevb.40.6611] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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