Consistent low-energy reduction of the three-band model for copper oxides with O-O hopping to the effective<i>t</i>-<i>J</i>model

Belinicher, V. I.; Chernyshev, A. L.

doi:10.1103/physrevb.49.9746

Cited by 72 publications

(68 citation statements)

References 24 publications

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“…This suggests that the dispersion should somehow be related to an effective nnn hopping which must be present even when t ′ = 0. While this effective long-range hopping is not explicitly present in the Hubbard model when t ′ = 0, it does appear in a t/U expansion to lowest order [47][48][49][50] as the so-called 3-site term, see Fig. 3(a) and Refs.…”

Section: The 2d Hubbard Model Hamiltonian H H Ismentioning

confidence: 99%

Origin of strong dispersion in Hubbard insulators

et al. 2015

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Using cluster perturbation theory, we explain the origin of the strongly dispersive feature found at high binding energy in the spectral function of the Hubbard model. By comparing the Hubbard and t−J−3s model spectra, we show that this dispersion does not originate from either coupling to spin fluctuations (∝ J) or the free hopping (∝ t). Instead, it should be attributed to a long-range, correlated hopping ∝ t 2 /U , which allows an effectively free motion of the hole within the same antiferromagnetic sublattice. This origin explains both the formation of the high energy anomaly in the single-particle spectrum and the sensitivity of the high binding energy dispersion to the next-nearest-neighbor hopping t ′ .PACS numbers: 71.10. Fd, 74.72.Cj, I. INTORDUCTIONHigh-temperature superconductivity in the cuprate oxides has attracted significant attention over the past thirty years. However, the precise origin of this phenomenon is not well understood due to the complex physics even in a minimal model used to describe the correlated nature of the electrons [1][2][3] : the 2D Hubbard model. It is often assumed that a first step in understanding the physics of this model is to study its spectral properties 4-17 in the simple undoped limit. The spectral function of the undoped 2D Hubbard model when the free electron bandwidth W is comparable to the Hubbard interaction U consists of two prominent features in the band structure, cf. Fig. 1. At low binding energies (LBE), a sharply defined quasiparticle-like excitation disperses downward from (π/2, π/2) reaching an energy of the order of spin exchange J = 4t 2 /U near the Γ-point (0,0). This quasiparticle, often labeled the spin polaron (SP) 18 , represents a hole heavily dressed by spin excitations from the antiferromagnetic (AF) ground state with its bandwidth no longer governed by the free electron hopping t but by the spin exchange J 9,18-23 . At higher binding energies (HBE), another feature becomes prominent approaching the Γ-point. The delineation of the LBE spin polaron from the HBE feature has been widely associated with the "high energy anomaly" or "waterfall" seen in a number of cuprate photoemission results 11,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] . While the spin polaron is well understood, the characterization remains poor for the feature at higher energies. One may naively expect that a broad, non-dispersive Hubbard band should appear at the Γ-point. However, as shown in Fig. 1, it is clear that there is a sharp dispersion. Previous studies have attributed this feature to scenarios such as spin-charge separation 16,17,34,35,[41][42][43][44][45] or a weak-coupling spin-density wave 9,10,46 . However, these interpretations remain controversial.The aim of this paper is to understand the nature of the HBE feature and what separates it from the SP. Using cluster perturbation theory we examine both the Hubbard, t−J and t−J−3s models to provide an in-depth examination of what controls the quasiparticle dispersion and int...

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Section: The 2d Hubbard Model Hamiltonian H H Ismentioning

confidence: 99%

Origin of strong dispersion in Hubbard insulators

et al. 2015

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“…However, the cuprate plane has long been known to be very poorly described by lowest-order perturbative approaches, and this has led to detailed efforts to derive more accurate low-energy descriptions from d-p [36] or three-band [37] models for the Cu and O orbitals. For clarity, we follow the systematic extension of the lowest-order analysis [30], where the direct in-plane O-O hopping, described by the overlap integral t pp , contributes to J through many possible fifth-and sixthorder processes.…”

Section: A Estimation Of Superexchange Parametersmentioning

confidence: 99%

Quantum and thermal ionic motion, oxygen isotope effect, and superexchange distribution inLa2CuO4

et al. 2014

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We study the zero-point and thermal ionic motion in La 2 CuO 4 by means of high-resolution neutron-diffraction experiments. Our results demonstrate anisotropic motion of O and, to a lesser extent, Cu ions, both consistent with the structure of coupled CuO 6 octahedra, and quantify the relative effects of zero-point and thermal contributions to ionic motion. By substitution of 18 O, we find that the oxygen isotope effect on the lattice dimensions is small and negative (−0.01%), while the isotope effect on the ionic displacement parameters is significant (−6 to 50%). We use our results as input for theoretical estimates of the distribution of magnetic interaction parameters, J , in an effective one-band model for the cuprate plane. We find that ionic motion causes only small (1%) effects on the average value J , which vary with temperature and O isotope, but results in dramatic (10-20%) fluctuations in J values that are subject to significant (8-12%) isotope effects. We demonstrate that this motional broadening of J can have substantial effects on certain electronic and magnetic properties in cuprates.

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“…In the study of the electronic structure of cuprates, correlation effects have been almost exclusively treated in the framework of model Hamiltonians. 16,46,47 Our estimation of the importance of electronic correlation contribution to J is obtained from the exact nonrelativistic Hamiltonian and, therefore, without making reference to the importance of any term entering into the definition of the electronic Hamiltonian. In the present work, the terms explicitly considered are, of course, those already defined in Anderson's original work.…”

Section: -29mentioning

confidence: 99%

“…A detailed study of the three-band model in the ''realistic'' region of the parameters has been reported recently. 16 In both, single-band and three-band models, perturbation theory is often used to obtain the magnetic coupling constant. In the first case, and up to second order, one obtains the Jϭ4t 2 /U expression corresponding to the original Anderson superexchange theory.…”

Section: Introductionmentioning

confidence: 99%

Origin of magnetic coupling inLa2CuO4

1996

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The ab initio cluster model approach has been used to study the origin of the magnetic coupling in La 2 CuO 4 and, also, its pressure dependence. Use of different cluster models and different ab initio wave functions permits the identification of the three leading mechanisms of magnetic coupling. These are the delocalization of the magnetic orbitals into the anion ''p'' band, the electronic correlation effects, and the collective effects hidden in the two-body operator of the Heisenberg Hamiltonian. The first two mechanisms are almost equally important and account for 80% of the experimental magnetic coupling constant value, the remaining 20% being due to the third effect. For the pressure dependence we predict Jϰr Ϫn with nϷ8.4 in agreement with experiment. Surprisingly enough these mechanisms are exactly the same previously found for KNiF 3 but with different contributions to the value of the magnetic coupling constant.

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Consistent low-energy reduction of the three-band model for copper oxides with O-O hopping to the effectivet-Jmodel

Cited by 72 publications

References 24 publications

Origin of strong dispersion in Hubbard insulators

Origin of strong dispersion in Hubbard insulators

Quantum and thermal ionic motion, oxygen isotope effect, and superexchange distribution inLa2CuO4

Origin of magnetic coupling inLa2CuO4

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