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arXiv:cond-mat/0003465

Effect of Exclusion of Double Occupancies in t-J Model: Extension of Gutzwiller Approximation

Masao Ogata, Akihiro Himeda

Published Mar 29, 2000• 0 citations
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Abstract

A new type of analytic estimation of the effect of strong correlation is developed for the two-dimensional t-J model. It is based on the Gutzwiller approximation which gives the renormalization of parameters, t and J, due to the Gutzwiller's projection operator excluding the double occupancies. The finite-range correlations are taken into account compared with the conventional Gutzwiller approximation where only the on-site expectation values are considered. It is shown that the essential point of the renormalization is its nonlinear dependence on the expectation values of Cooper pairs and antiferromagnetic moment. In particular the renormalization factor of J becomes anisotropic in the presence of antiferromagnetic moment, i.e., that for the z-component is enhanced compared with that for the xy-component. The physical origin of this enhancement is identified as the surrounding antiferromagnetic correlations of a bond. The self-consistency equations for the uniform variational wave functions are derived and solved numerically. Our result gives a reasonable estimate of antiferromagnetic order parameters near half filling, in contrast to the conventional slave-boson mean-field theory and the original Gutzwiller approximation. It is also found that, at half filling, the renormalization of J represents some of the quantum fluctuations of the Heisenberg spin system in a different manner from the spin-wave theory. For finite doping, our results have some similarity to SO(5) symmetric theory. Applications to the inhomogeneous systems such as the vortex state, around nonmagnetic impurities, and stripe state are discussed.

DOI
10.48550/arxiv.cond-mat/0003465

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arXiv:cond-mat/0008384•Aug 25, 2000•0 citations
A new type of analytic estimation of the effect of strong correlation is developed for the two-dimensional t-J model. It is based on the Gutzwiller approximation which gives the renormalization of parameters, t and J, due to the Gutzwiller's projection operator excluding the double occupancies. The finite-range correlations are taken into account compared with the conventional Gutzwiller approximation where only the on-site expectation values are considered. It is shown that the essential point of the renormalization is its nonlinear dependence on the expectation values of Cooper pairs and antiferromagnetic moment. In particular the renormalization factor of J becomes anisotropic in the presence of antiferromagnetic moment, i.e., that for the z-component is enhanced compared with that for the xy-component. The physical origin of this enhancement is identified as the surrounding antiferromagnetic correlations of a bond. The self-consistency equations for the uniform variational wave functions are derived and solved numerically. Our result gives a reasonable estimate of antiferromagnetic order parameters near half filling, in contrast to the conventional slave-boson mean-field theory and the original Gutzwiller approximation. It is also found that, at half filling, the renormalization of J represents some of the quantum fluctuations of the Heisenberg spin system in a different manner from the spin-wave theory. For finite doping, our results have some similarity to SO(5) symmetric theory. Applications to the inhomogeneous systems such as the vortex state, around nonmagnetic impurities, and stripe state are discussed.
The ground state of two-dimensional t – J model including superconductivity and antiferromagnetism is studied using a new type of analytic estimation of the effect of strong correlation. The method is an extension of the Gutzwiller approximation which gives renormalization of parameters, t and J , due to the Gutzwiller projection operator excluding double occupancies. It is shown that the essential point of the renormalization is its dependence on the expectation values of superconductivity and antiferromagnetic moment. In special the renormalization factor is anisotropic in spin space, which leads to a reliable estimate of antiferromagnetic order parameters in the phase diagram, in contrast to the conventional slave-boson mean-field theory. The obtained phase diagram shows the coexistence of antiferromagnetism and d x 2 - y 2 -wave superconductivity for the doping rate, δ, less than 10%. At half-filling, the renormalization of the J -term represents some aspects of quantum spin nature. For the finite doping case, there are two kinds of superconducting order parameters. The variational order parameter of the d-wave superconductivity increases as the doping rate decreases, which will correspond to the experimentally observed superconducting gap. In contrast, the actual expectation value of superconducting order parameter is proportional to δ in underdoped region and has a maximum near δ=0.11, which probably determines T c . We also speculate that the ground-state antiferromagnetic order, being destroyed at finite temperatures, gives the energy and temperature scale of the pseudogap. Applications to the inhomogeneous systems such as the vortex state and stripe state are discussed.
Extended t-t'-t"-J-U models in which the second-nearest-neighbor hopping (t') and third-nearest-neighbor hopping (t") are included are studied using renormalized mean field theory. The models are meant to be low-energy effective models for the Hubbard models, and hence the Heisenberg exchange integral J and Hubbard repulsion U are related by J = 4t(2)/U. The trial wavefunctions for the ground states are partially Gutzwiller projected Hartree-Fock states. The Gutzwiller projection is implemented by means of a Gutzwiller approximation, and the site double occupancy d is taken as a variational parameter. It is found that a large |t'/t| narrows the band filling range that sustains antiferromagnetism (AFM) in the ground state, enhances the d-wave singlet superconductivity (dSC) in hole overdoped systems, but suppresses the dSC in electron overdoped systems. For a system that has large |t'/t| and |t"/t'|, the superconductivity (SC) at the onset of AFM in hole doped band filling is strongly suppressed. On the excitation occurring, when an electron doped system simultaneously contains SC and AFM, the system is found to have a nodeless gap at the Fermi level. Finally, the result of this study is related to experiments on the superconducting cuprates.
The coexisting phase of the d-wave superconducting and the antiferromagnetic order in the two-dimensional t-JJJ model is reexamined using a variational Monte Carlo method in order to estimate the Gutzwiller factors. A trial wave function is used which is consistent with the mean-field solution. The Gutzwiller factors are determined by comparing the numerically obtained expectation values with the mean-field values. We find the z component of the Gutzwiller factor of exchange interaction is enhanced compared with the xy\mathrm{xy}xy components. This effect does not appear in the conventional Gutzwiller approximation and is essential for the stabilization of the antiferromagnetic order in the presence of d-wave superconductivity. We discuss several applications of the present Gutzwiller factors to the problems with antiferromagnetism and d-wave superconductivity.
We investigate a connection between the $t\text{\ensuremath{-}}J$ model and the strongly correlated Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, with the effect of strong electron correlations accounted by the Gutzwiller projection. We show that in the immediate vicinity of half filling the projected two-dimensional BCS Hamiltonian with strong pairing develops an antiferromagnetically ordered ground state. This result explicitly demonstrates that antiferromagnetism in this model appears as a natural consequence of the strong Coulomb repulsion in a low doped regime. At moderate doping the ground state of the Gutzwiller-projected BCS Hamiltonian is, in finite-system studies, known to become qualitatively similar to Anderson's resonating valence bond state which, in turn, fits nicely with the properties of the $t\text{\ensuremath{-}}J$ model in that regime. Combined together, these two properties indicate that the projected BCS Hamiltonian at least qualitatively captures the essential low-energy physics of the $t\text{\ensuremath{-}}J$ model in the underdoped region.
We investigate analytically a connection between the t-J model and the strongly correlated Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, with the effect of strong electron correlations accounted by the Gutzwiller projection. We show that in the immediate vicinity of half filling the projected 2D BCS Hamiltonian with strong pairing develops an antiferromagnetically (AF) ordered ground state. This result explicitly demonstrates that antiferromagnetism in this model appears as a natural consequence of the strong Coulomb repulsion in a low doped regime. At moderate doping the ground state of the Gutzwiller-projected BCS Hamiltonian becomes qualitatively similar to Anderson's resonating valence bond state which is known to fit nicely the properties of the t-J model in this regime. These two properties taken together indicate that the projected BCS Hamiltonian captures the essential low-energy physics of the t-J model in the whole underdoped region.
New interpretation of slave boson mean-field theory of the t−Jt-Jt−J model: short-range antiferromagnetic and d-wave pairing correlations
The t−Jt-Jt−J Hamiltonian is studied in a mean-field approximation by taking into account antiferromagnetic and d-wave pairing correlations. Considering the presence of antiferromagnetic fluctuations, the weaknesses of a mean-field approximation and the limitation of the t−Jt-Jt−J model near half-filling, we give a new interpretation to the slave boson mean-field theory of the t−Jt-Jt−J model. We argue that due to phase coherence-breaking antiferromagnetic fluctuations and quantum fluctuations, superconducting long-range order does not appear strictly in two dimensions. TcT_{c}Tc​ resulting from interlayer pairing hopping can lead to a universal relation, when TcT_{c}Tc​ is scaled by TcmaxT^{max}_{c}Tcmax​. Systematic reduction of superfluid density and increase of (Δd)max/KBTc(Δ_{d})_{max}/K_{B}T_{c}(Δd​)max​/KB​Tc​ ratio below and near optimal doping have their natural explanation in our picture. A crossover temperature T0T^{0}T0 found in some of magnetic experiments such as NMR is also easily understood in the present framework.