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Wang CY, Ho TL. Interference of holon strings in 2D Hubbard model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:175402. [PMID: 38232392 DOI: 10.1088/1361-648x/ad1f8d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 01/17/2024] [Indexed: 01/19/2024]
Abstract
The 2D Hubbard model with large repulsion is an important problem in condensed matter physics. At half filling, its ground state is an antiferromagnet (AMF). The dope AMF below half filling is believed to capture the physics of highTcsuperconductors. And the fermion excitation of this dope AMF is theorized as splitting up into holons and spinons that carry charge and spin separately. It is believed that these exotic holons and spinons are the origins of the unusual properties of highTcsuperconductors. Despite the interests in holons and spinons, the direct observations of these excitations remain difficult in solid state experiments. Here, we show that with the rapid advances in the experimental techniques in cold atoms, the direct observation of holons is possible in quantum quench dynamic processes in cold atom settings. We show that the well-known holon-strings generated by the motion of a holon as well as their interferences can be detected by the measurements spin-spin correlations and demonstrate the presence of the Marshall phase associated with a holon string reflecting an underlying AMF background. Moreover, we show that the interferences of the holon strings make a holon propagate anisotropically, with a diffusion pattern clearly distinct from that of spinless fermions. At the same time, we show that these interferences lead to a large suppression in magnetic order in the region swept through by the strings (even to about 95% for some bond). We further demonstrate the Marshall phase of the holon-strings by comparing the dynamics of holon in thetJmodel with that of the so-calledσtJ-model, which is thetJmodel with the Marshall phase removed. The holons in these models propagate entirely differently.
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Affiliation(s)
- Chang-Yan Wang
- Department of Physics, The Ohio State University, Columbus, OH 43210, United States of America
| | - Tin-Lun Ho
- Department of Physics, The Ohio State University, Columbus, OH 43210, United States of America
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2
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Lu H, Rossi M, Nag A, Osada M, Li DF, Lee K, Wang BY, Garcia-Fernandez M, Agrestini S, Shen ZX, Been EM, Moritz B, Devereaux TP, Zaanen J, Hwang HY, Zhou KJ, Lee WS. Magnetic excitations in infinite-layer nickelates. Science 2021; 373:213-216. [DOI: 10.1126/science.abd7726] [Citation(s) in RCA: 50] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2020] [Revised: 09/08/2020] [Accepted: 05/21/2021] [Indexed: 11/03/2022]
Affiliation(s)
- H. Lu
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
- Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, CA 94305, USA
| | - M. Rossi
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
| | - A. Nag
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, UK
| | - M. Osada
- Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, CA 94305, USA
| | - D. F. Li
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
| | - K. Lee
- Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, CA 94305, USA
| | - B. Y. Wang
- Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, CA 94305, USA
| | | | - S. Agrestini
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, UK
| | - Z. X. Shen
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
- Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, CA 94305, USA
| | - E. M. Been
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
| | - B. Moritz
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
| | - T. P. Devereaux
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
- Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, CA 94305, USA
- Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA
| | - J. Zaanen
- Instituut-Lorentz for theoretical Physics, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, Netherlands
| | - H. Y. Hwang
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
- Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, CA 94305, USA
| | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, UK
| | - W. S. Lee
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
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Schmehr JL, Mion TR, Porter Z, Aling M, Cao H, Upton MH, Islam Z, He RH, Sensarma R, Trivedi N, Wilson SD. Overdamped Antiferromagnetic Strange Metal State in Sr_{3}IrRuO_{7}. PHYSICAL REVIEW LETTERS 2019; 122:157201. [PMID: 31050510 DOI: 10.1103/physrevlett.122.157201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2018] [Revised: 01/24/2019] [Indexed: 06/09/2023]
Abstract
The unconventional electronic ground state of Sr_{3}IrRuO_{7} is explored via resonant x-ray scattering techniques and angle-resolved photoemission measurements. As the Ru content approaches x=0.5 in Sr_{3}(Ir_{1-x}Ru_{x})_{2}O_{7}, intermediate to the J_{eff}=1/2 Mott state in Sr_{3}Ir_{2}O_{7} and the quantum critical metal in Sr_{3}Ru_{2}O_{7}, a thermodynamically distinct metallic state emerges. The electronic structure of this intermediate phase lacks coherent quasiparticles, and charge transport exhibits a linear temperature dependence over a wide range of temperatures. Spin dynamics associated with the long-range antiferromagnetism of this phase show nearly local, overdamped magnetic excitations and an anomalously large energy scale of 200 meV-an energy far in excess of exchange energies present within either the Sr_{3}Ir_{2}O_{7} or Sr_{3}Ru_{2}O_{7} solid-solution end points. Overdamped quasiparticle dynamics driven by strong spin-charge coupling are proposed to explain the incoherent spectral features of the strange metal state in Sr_{3}IrRuO_{7}.
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Affiliation(s)
- Julian L Schmehr
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - Thomas R Mion
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
| | - Zach Porter
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - Michael Aling
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - Huibo Cao
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Mary H Upton
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Zahirul Islam
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Rui-Hua He
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
| | - Rajdeep Sensarma
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India
| | - Nandini Trivedi
- Mathematics Department, The Ohio State University, Columbus, Ohio 43210, USA
| | - Stephen D Wilson
- Materials Department, University of California, Santa Barbara, California 93106, USA
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Pärschke EM, Wohlfeld K, Foyevtsova K, van den Brink J. Correlation induced electron-hole asymmetry in quasi- two-dimensional iridates. Nat Commun 2017; 8:686. [PMID: 28947738 PMCID: PMC5612937 DOI: 10.1038/s41467-017-00818-8] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2017] [Accepted: 07/25/2017] [Indexed: 11/09/2022] Open
Abstract
The resemblance of crystallographic and magnetic structures of the quasi-two-dimensional iridates Ba2IrO4 and Sr2IrO4 to La2CuO4 points at an analogy to cuprate high-Tc superconductors, even if spin-orbit coupling is very strong in iridates. Here we examine this analogy for the motion of a charge (hole or electron) added to the antiferromagnetic ground state. We show that correlation effects render the hole and electron case in iridates very different. An added electron forms a spin polaron, similar to the cuprates, but the situation of a removed electron is far more complex. Many-body 5d 4 configurations form which can be singlet and triplet states of total angular momentum that strongly affect the hole motion. This not only has ramifications for the interpretation of (inverse-)photoemission experiments but also demonstrates that correlation physics renders electron- and hole-doped iridates fundamentally different.Some iridate compounds such as Sr2IrO4 have electronic and atomic structures similar to quasi-2D copper oxides, raising the prospect of high temperature superconductivity. Here, the authors show that there is significant electron-hole asymmetry in iridates, contrary to expectations from the cuprates.
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Affiliation(s)
| | - Krzysztof Wohlfeld
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, PL-02093, Warsaw, Poland
| | - Kateryna Foyevtsova
- University of British Columbia, 6224 Agricultural Road, Vancouver, BC, Canada, V6T 1Z1
| | - Jeroen van den Brink
- IFW Dresden, Helmholtzstr. 20, 01069, Dresden, Germany.,Institute for Theoretical Physics, TU Dresden, 01069, Dresden, Germany
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Plotnikova EM, Daghofer M, van den Brink J, Wohlfeld K. Jahn-Teller Effect in Systems with Strong On-Site Spin-Orbit Coupling. PHYSICAL REVIEW LETTERS 2016; 116:106401. [PMID: 27015495 DOI: 10.1103/physrevlett.116.106401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2015] [Indexed: 06/05/2023]
Abstract
When strong spin-orbit coupling removes orbital degeneracy, it would at the same time appear to render the Jahn-Teller mechanism ineffective. We discuss such a situation, the t_{2g} manifold of iridates, and show that, while the Jahn-Teller effect does indeed not affect the j_{eff}=1/2 antiferromagnetically ordered ground state, it leads to distinctive signatures in the j_{eff}=3/2 spin-orbit exciton. It allows for a hopping of the spin-orbit exciton between the nearest-neighbor sites without producing defects in the j_{eff}=1/2 antiferromagnet. This arises because the lattice-driven Jahn-Teller mechanism only couples to the orbital degree of freedom but is not sensitive to the phase of the wave function that defines isospin j_{z}. This contrasts sharply with purely electronic propagation, which conserves isospin, and the presence of Jahn-Teller coupling can explain some of the peculiar features of measured resonant inelastic x-ray scattering spectra of Sr_{2}IrO_{4}.
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Affiliation(s)
- Ekaterina M Plotnikova
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Maria Daghofer
- Institute for Functional Materials and Quantum Technologies, University of Stuttgart, Pfaffenwaldring 57 D-70550 Stuttgart, Germany
| | - Jeroen van den Brink
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
- Institute for Theoretical Physics, TU Dresden, 01069 Dresden, Germany
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Krzysztof Wohlfeld
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, 2575 Sand Hill Road, Menlo Park, California 94025, USA
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, PL-02093 Warsaw, Poland
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6
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Persistent spin excitations in doped antiferromagnets revealed by resonant inelastic light scattering. Nat Commun 2014; 5:3314. [PMID: 24577074 DOI: 10.1038/ncomms4314] [Citation(s) in RCA: 108] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2013] [Accepted: 01/24/2014] [Indexed: 11/08/2022] Open
Abstract
How coherent quasiparticles emerge by doping quantum antiferromagnets is a key question in correlated electron systems, whose resolution is needed to elucidate the phase diagram of copper oxides. Recent resonant inelastic X-ray scattering (RIXS) experiments in hole-doped cuprates have purported to measure high-energy collective spin excitations that persist well into the overdoped regime and bear a striking resemblance to those found in the parent compound, challenging the perception that spin excitations should weaken with doping and have a diminishing effect on superconductivity. Here we show that RIXS at the Cu L3-edge indeed provides access to the spin dynamical structure factor once one considers the full influence of light polarization. Further we demonstrate that high-energy spin excitations do not correlate with the doping dependence of Tc, while low-energy excitations depend sensitively on doping and show ferromagnetic correlations. This suggests that high-energy spin excitations are marginal to pairing in cuprate superconductors.
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Oleś AM. Fingerprints of spin-orbital entanglement in transition metal oxides. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:313201. [PMID: 22776856 DOI: 10.1088/0953-8984/24/31/313201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The concept of spin-orbital entanglement on superexchange bonds in transition metal oxides is introduced and explained on several examples. It is shown that spin-orbital entanglement in superexchange models destabilizes the long-range (spin and orbital) order and may lead either to a disordered spin-liquid state or to novel phases at low temperature which arise from strongly frustrated interactions. Such novel ground states cannot be described within the conventionally used mean field theory which separates spin and orbital degrees of freedom. Even in cases where the ground states are disentangled, spin-orbital entanglement occurs in excited states and may become crucial for a correct description of physical properties at finite temperature. As an important example of this behaviour we present spin-orbital entanglement in the RV O(3) perovskites, with R = La,Pr,…,Y b,Lu, where the finite temperature properties of these compounds can be understood only using entangled states: (i) the thermal evolution of the optical spectral weights, (ii) the dependence of the transition temperatures for the onset of orbital and magnetic order on the ionic radius in the phase diagram of the RV O(3) perovskites, and (iii) the dimerization observed in the magnon spectra for the C-type antiferromagnetic phase of Y V O(3). Finally, it is shown that joint spin-orbital excitations in an ordered phase with coexisting antiferromagnetic and alternating orbital order introduce topological constraints for the hole propagation and will thus radically modify the transport properties in doped Mott insulators where hole motion implies simultaneous spin and orbital excitations.
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Affiliation(s)
- Andrzej M Oleś
- Marian Smoluchowski Institute of Physics, Jagellonian University, Kraków, Poland.
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Maśka MM, Mierzejewski M, Ferraz A, Kochetov EA. Ising t-J model close to half filling: a Monte Carlo study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:045703. [PMID: 21715821 DOI: 10.1088/0953-8984/21/4/045703] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t-J model. This model possesses the global discrete Z(2) symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t-J model, usually referred to as the t-J(z) model, the global SU(2) invariance is fully restored at J(z) = 0, so that only the spin-spin interaction has in this model the true Ising form. We discuss a relationship between these two models and the standard isotropic t-J model. We show that the low-energy quasiparticles in all three models share qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t-J model over the t-J(z) one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10(3) sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next-nearest-neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no-double-occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed.
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Affiliation(s)
- M M Maśka
- Department of Theoretical Physics, Institute of Physics, University of Silesia, 40-007 Katowice, Poland
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Daghofer M, Wohlfeld K, Oleś AM, Arrigoni E, Horsch P. Absence of hole confinement in transition-metal oxides with orbital degeneracy. PHYSICAL REVIEW LETTERS 2008; 100:066403. [PMID: 18352494 DOI: 10.1103/physrevlett.100.066403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2007] [Indexed: 05/26/2023]
Abstract
We investigate the spectral properties of a hole moving in a two-dimensional Hubbard model for strongly correlated t(2g) electrons. Although superexchange interactions are Ising-like, a quasi-one-dimensional coherent hole motion arises due to effective three-site terms. This mechanism is fundamentally different from the hole motion via quantum fluctuations in the conventional spin model with SU(2) symmetry. The orbital model describes also propagation of a hole in some e(g) compounds, and we argue that orbital degeneracy alone does not lead to hole self-localization.
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Affiliation(s)
- Maria Daghofer
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
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Mishchenko AS, Nagaosa N. Electron-phonon coupling and a polaron in the t-J model: from the weak to the strong coupling regime. PHYSICAL REVIEW LETTERS 2004; 93:036402. [PMID: 15323844 DOI: 10.1103/physrevlett.93.036402] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2003] [Indexed: 05/24/2023]
Abstract
We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for a single hole in the t-J model coupled to optical phonons. The systematic-error-free diagrammatic Monte Carlo method is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonon variables, while magnetic variables are subjected to the noncrossing approximation. We obtain that at electron-phonon coupling constants relevant for high T(c) cuprates the polaron undergoes a self-trapping crossover to the strong-coupling limit and theoretical ARPES demonstrate features observed in experiment: A broad peak in the bottom of the spectra has momentum dependence which coincides with that of a hole in the pure t-J model.
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Affiliation(s)
- A S Mishchenko
- CREST, Japan Science and Technology Agency (JST), AIST, 1-1-1, Higashi, Tsukuba 305-8562, Japan
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Belinicher VI, Chernyshev AL, Shubin VA. Single-hole dispersion relation for the real CuO2 plane. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:14914-14917. [PMID: 9985535 DOI: 10.1103/physrevb.54.14914] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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12
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Eskes H, Eder R. Hubbard model versus t-J model: The one-particle spectrum. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:R14226-R14229. [PMID: 9985493 DOI: 10.1103/physrevb.54.r14226] [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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13
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Kyung B, Ferrell RA. Quasiparticle dispersion of the insulating copper oxide Sr2CuO2Cl2 by employing vertical and horizontal double hoppings. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:10125-10130. [PMID: 9984752 DOI: 10.1103/physrevb.54.10125] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bala J, Oles AM, Zaanen J. Quasiparticles in the spin-fermion model for CuO2 planes. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:10161-10174. [PMID: 9984757 DOI: 10.1103/physrevb.54.10161] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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15
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Bala J, Oles AM. Quasiparticle band in the frustrated t-t'-J model. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:3495-3498. [PMID: 9986251 DOI: 10.1103/physrevb.54.3495] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Feiner LF, Jefferson JH, Raimondi R. Intrasublattice Hopping in the Extended t-J Model and Tmaxc in the Cuprates. PHYSICAL REVIEW LETTERS 1996; 76:4939-4942. [PMID: 10061418 DOI: 10.1103/physrevlett.76.4939] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Raimondi R, Jefferson JH, Feiner LF. Effective single-band models for the high-Tc cuprates. II. Role of apical oxygen. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:8774-8788. [PMID: 9982390 DOI: 10.1103/physrevb.53.8774] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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18
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Belinicher VI, Chernyshev AL, Shubin VA. Generalized t-t'-J model: Parameters and single-particle spectrum for electrons and holes in copper oxides. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:335-342. [PMID: 9981982 DOI: 10.1103/physrevb.53.335] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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