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arXiv:1903.09368 · Journal of the Physical Society of Japan

Antiferromagnetism, Superconductivity and Phase Diagram in the Two-Dimensional Hubbard Model —Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model III—

Takashi Yanagisawa

Published Apr 5, 2019• 13 citations
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Abstract

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 $ψ=\exp(-λK)P_Gψ_0$, where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ 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 $U$, the band parameter $t'$ and the electron density $n_e$. We show a phase diagram that includes superconducting and antiferromagnetic phases and that $t'=0$ is most favorable for superconductivity.

DOI
10.7566/jpsj.88.054702

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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.
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We investigate the ground state of the two-dimensional single-band Hubbard model and three-band Hubbard model (d-p model) by using a variational Monte Carlo method. We employ an optimization variational Monte Carlo method. In this method the many-body wave function is improved and optimized by introducing variational parameters in the form: ψ = exp(- S ) ψ 0 where ψ 0 is a wave function, for example, the Gutzwiller function, and S is an operator used to include the many-body effect. The strong magnetic correlation is induced by the on-site Coulomb repulsive interaction U . The magnetic correlation plays a significant role in correlated electron systems as an origin of electron pairing as well as a main competitor of superconductivity. High-temperature superconductivity occurs in the strongly correlated region where U is greater than the bandwidth. We investigate the stability of antiferromagnetic state in the three-band d-p model.
We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp(−S-S−S)-type where SSS is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The ddd-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the ddd-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.
We investigate the ground state of two-dimensional Hubbard model on the basis of the variational Monte Carlo method. We use wave functions that include kinetic correlation and doublon-holon correlation beyond the Gutzwiller ansatz. It is still not clear whether the Hubbard model accounts for high-temperature superconductivity. The antiferromagnetic correlation plays a key role in the study of pairing mechanism because the superconductive phase exists usually close to the antiferromagnetic phase. We investigate the stability of the antiferromagnetic state when holes are doped as a function of the Coulomb repulsion U . We show that the antiferromagnetic correlation is suppressed as U is increased exceeding the bandwidth. High-temperature superconductivity is possible in this region with enhanced antiferromagnetic spin fluctuation and pairing interaction.
A variational Monte-Carlo method is formulated to study superconductivity in strongly correlated electrons. An application is made to the strongly correlated Hubbard model on two-dimensional square lattice, by employing the simplest mean-field-type trial wave function, i.e. the Gutzwiller-projected BCS wave function. Among the various choices examined, the d-wave-type superconductivity turns out to be the most favorable. The nature of the superconducting order parameter and spin correlations is also examined.