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Physical review. B, Condensed matter

Normal and antiferromagnetic states of an extended Hubbard model

S. N. Coppersmith

Published May 1, 1990• 14 citations
Publisher

Abstract

Variational Monte Carlo calculations using extensions of the Gutzwiller variational wave function are used to study the phase diagram of an extended Hubbard model on a copper-oxygen lattice in two dimensions. Antiferromagnetism appears to occur at half-filling only when the oxygen p levels and copper d levels have substantially different energies. It is also found that strong nearest-neighbor repulsions can enhance the tendency for local-moment antiferromagnetism. The dependence of the variational parameters on the Hamiltonian parameters, particularly nearest-neighbor repulsions, is examined. The implications for models of high-temperature superconductivity are discussed.

DOI
10.1103/physrevb.41.8711

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Variational Monte Carlo calculations using extensions of the Gutzwiller variational wave function are used to study the phase diagram of an extended Hubbard model on a copper-oxygen lattice in two dimensions. Antiferromagnetism appears to occur at half-filling only when the oxygen p levels and copper d levels have substantially different energies. It is also found that strong nearest-neighbor repulsions can enhance the tendency for local-moment antiferromagnetism. The dependence of the variational parameters on the Hamiltonian parameters, particularly nearest-neighbor repulsions, is examined. The implications for models of high-temperature superconductivity are discussed.
The variational Monte Carlo method is used to study possible superconducting states of a two-dimensional extended Hubbard model on a copper-oxygen lattice. It is found that d-wave and extended s-wave superconducting variational wave functions can have lower energy than the corresponding normal state for different parameter regions, while simple s-wave superconductivity is never favored. Increasing the nearest-neighbor repulsion and decreasing the copper-oxygen level separation can promote extended s-wave superconductivity and inhibit d-wave superconductivity.
We explore the phase diagram of the Hubbard model by generalizing the Gutzwiller variational wave function to take into account nearest-neighbor spin correlations. The energies of various variational states are calculated and compared. At half filling the lowest energy state has long-range antiferromagnetic correlations, in agreement with previous results. Away from half filling, when the antiferromagnet no longer has the lowest energy, the Gutzwiller approximation yields a lower energy than that found for small spin polarons.
We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as ψ=exp⁡(−λK)PGψ0ψ=\exp(-λK)P_Gψ_0ψ=exp(−λK)PG​ψ0​, where ψ0ψ_0ψ0​ is a one-particle state, PGP_GPG​ is the Gutzwiller operator, KKK is the kinetic operator, and λλλ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion UUU, the band parameter t′t't′ and the electron density nen_ene​. We show a phase diagram that includes superconducting and antiferromagnetic phases and that t′=0t'=0t′=0 is most favorable for superconductivity.
It is important to understand the phase diagram of electronic states in the CuO2 plane to clarify the mechanism of high-temperature superconductivity. We investigate the ground state of electronic models with strong correlation by employing the optimization variational Monte Carlo method. We consider the two-dimensional Hubbard model as well as the three-band [Formula: see text]–[Formula: see text] model. We use the improved wave function that takes account of inter-site electron correlation to go beyond the Gutzwiller wave function. The ground state energy is lowered considerably, which now gives the best estimate of the ground state energy for the two-dimensional Hubbard model. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We investigate the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion [Formula: see text], the band parameter [Formula: see text] and the electron density [Formula: see text] for the Hubbard model. We show phase diagrams that include superconducting and antiferromagnetic phases. We expect that high-temperature superconductivity occurs near the boundary between antiferromagnetic phase and superconducting one. Since the three-band [Formula: see text]–[Formula: see text] model contains many-band parameters, high-temperature superconductivity may be more likely to occur in the [Formula: see text]–[Formula: see text] model than in single-band models.
Abstract We investigate the ground state of the two-dimensional three-band d-p model for for high-temperature superconductors on the basis of a variational Monte Carlo method. We employ an optimization variational Monte Carlo method that we have developed recently. The many-body wave function is improved beyond the Gutzwiller ansatz by adopting the wave function in the form ψ = exp(−S)ψG where ψG represents the Gutzwiller function and S is a kinetic operator. The strong magnetic correlation and also superconductivity (SC) are induced by the on-site Coulomb repulsive interaction. It is important to clarify the phase diagram that includes superconductive phase and antiferromagnetic phase. We show the phase diagram to show the antiferromagnetic region in the parameter space. High-temperature superconductivity may occur in the strongly correlated region near the antiferromagnetic boundary.