Configuration-interaction approach to hole pairing in the two-dimensional Hubbard model

Louis, E.; Guinea, F.; Sancho, M. P. López; Vergés, J. A.

doi:10.1103/physrevb.59.14005

Cited by 22 publications

(27 citation statements)

References 49 publications

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“…C i,j shows a maximum (0.021) when the holes are separated by a vector r ij = r i − r j = (0, 2), that is when they are two lattice constants apart along the stripe direction. This feature of the hole-hole correlation differentiates stripes from other two hole configurations investigated within the t − J [22] or the Hubbard models [23,18]. We note, however, that C i,j is also rather large (0.011) for the hole-hole separation at which the results reported in those studies show the maximum hole-hole correlation, namely, r ij = (1, 1).…”

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confidence: 41%

“…In addition, one needs to consider quantum tunneling processes between degenerate, or nearly degenerate, Hartree-Fock solutions, when there are many. This is achieved with the Configuration Interaction method (CI), widely used in quantum chemistry [17,18]. The combination of the Hartree-Fock and CI methods gives reasonable results even when applied to one dimensional systems [19].…”

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confidence: 99%

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Partially filled stripes in the two-dimensional Hubbard model: Statics and dynamics

et al. 2001

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The internal structure of stripes in the two dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes, consistent with experimental observations, are stabilized by quantum fluctuations, included through the Configuration Interaction method. Hopping of short regions of the stripes in the transverse direction is comparable to the bare hopping element. The integrated value of n k compares well with experimental results.By now it is well established that charged stripes are formed in a significant doping range of cuprate oxides [1][2][3]. The existence of these stripes was predicted, on the basis of mean field calculations, in advance of its observation, both in the one [4][5][6][7] and the three bands Hubbard model [8]. This is one of the scarce theoretical results in the field of high-T c superconductivity which was confirmed after its prediction. Interest in these calculations decreased, as it was generally understood that the Hartree-Fock approximation was unable to obtain the partially filled stripes observed experimentally. Unrelated calculations found stripes with different fillings in the t-J model [9], and, using different techniques, in the Hubbard model [10], although other numerical calculations show conflicting results [11,12]. Alternatively, it has been argued that stripes in doped Mott antiferromagnets arise from a tendency towards phase separation, frustrated by electrostatic interactions [13,14]. Stripes in the Hubbard model have also been analyzed within slaveboson techniques, which use the Hartree-Fock solutions as input [15].In the present work we show that the mean field calculations, initially used to demonstrate the existence of stripes, can be systematically improved in order to study the partially filled stripes observed experimentally. In addition, they provide significant insight into the internal structure of the stripes and their fluctuations in the transverse direction. The Hartree-Fock method can be considered a quasiclassical approximation to the spin and charge degrees of freedom. Their low amplitude quantum fluctuations can be incorporated by using the Random Phase Approximation [16]. In addition, one needs to consider quantum tunneling processes between degenerate, or nearly degenerate, Hartree-Fock solutions, when there are many. This is achieved with the Configuration Interaction method (CI), widely used in quantum chemistry [17,18]. The combination of the Hartree-Fock and CI methods gives reasonable results even when applied to one dimensional systems [19]. The CI method restores the symmetries broken by the Hartree-Fock approximation, and provides information on the quantum dynamics of the static solutions obtained in mean field, which can be broadly classified into spin polarons or stripes.Previous mean field studies have focused on filled stripes [7], which tend to be the solutions with the lowest energy per hole in this approximation, especially for the values of U/t ∼ 4 used in the initial studies [4][5][6][7]. There are,...

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Partially filled stripes in the two-dimensional Hubbard model: Statics and dynamics

et al. 2001

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“…A possible solution to both problems is offered by the Configuration Interaction (CI) method. [62][63][64] In this approach, the ground state is constructed as a (biased) linear combination of HF solutions. This technique, which has already been applied to certain aspects of the isotropic Hubbard model, 63,51 can be shown to give a systematic description of quantum fluctuation and tunneling corrections to the HF solution, and of the quantum dynamics of the excitations.…”

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confidence: 99%

Lattice anisotropy as the microscopic origin of static stripes in cuprates

Normand

Kampf

2001

Phys. Rev. B

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Structural distortions in cuprate materials offer a microscopic origin for anisotropies in electron transport in the basal plane. Using a real-space Hartree-Fock approach, we consider the ground states of the anisotropic Hubbard (tx = ty) and t-J (tx = ty, Jx = Jy) models. Symmetrical but inhomogeneous ("polaronic") charge structures in the isotropic models are altered even by rather small anisotropies to one-dimensional, stripe-like features. We find two distinct types of stripe, namely uniformly filled, antiphase domain walls and non-uniform, half-filled, in-phase ones. We characterize their properties, energies and dependence on the model parameters, including filling and anisotropy in t (and J). We discuss the connections among these results, other theoretical studies and experimental observation.

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“…4 Given the fact that the set of all possible Slater determinants (with all possible occupation numbers) generated from a complete set of one-electron orbitals constitute a complete basis of the N e -particle Hilbert space, our aim is to pick out a subset of Slater determinants which captures the essential physics of the exact solution.…”

Section: B Configuration Interaction Methodsmentioning

confidence: 99%

Quantum dynamics of charged and neutral magnetic solitons: Spin-charge separation in the one-dimensional Hubbard model

Berciu

John

2000

Phys. Rev. B

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Nos. 71.27.+a, 71.10.Fd, 74.20.Mn We demonstrate that the Configuration Interaction (CI) Approximation recaptures essential features of the exact (Bethe Ansatz) solution to the 1D Hubbard model. As such, it provides valuable route for describing effects which go beyond mean-field theory for strongly correlated electron systems in higher dimensions. The CI method systematically describes fluctuation and quantum tunneling corrections to the Hartree-Fock Approximation (HFA). HFA predicts that doping a half-filled Hubbard chain leads to the appearance of charged spin-polarons or charged domain-wall solitons in the antiferromagnetic (AFM) background. The CI method, on the other hand, describes the quantum dynamics of these charged magnetic solitons and quantum tunneling effects between various mean-field configurations. In this paper, we test the accuracy of the CI method against the exact solution of the one-dimensional Hubbard model. We find remarkable agreement between the energy of the mobile charged bosonic domain-wall (as given by the CI method) and the exact energy of the doping hole (as given by the Bethe Ansatz) for the entire U/t range. The CI method also leads to a clear demonstration of the spin-charge separation in 1D. Addition of one doping hole to the half-filled antiferromagnetic chain results in the appearance of two different carriers: a charged bosonic domain-wall (which carries the charge but no spin) and a neutral spin-1/2 domain wall (which carries the spin but no charge).

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Configuration-interaction approach to hole pairing in the two-dimensional Hubbard model

Cited by 22 publications

References 49 publications

Partially filled stripes in the two-dimensional Hubbard model: Statics and dynamics

Partially filled stripes in the two-dimensional Hubbard model: Statics and dynamics

Lattice anisotropy as the microscopic origin of static stripes in cuprates

Quantum dynamics of charged and neutral magnetic solitons: Spin-charge separation in the one-dimensional Hubbard model

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