The ${\mathrm{CuO}}_{2}$ sheets common to the superconducting cuprates are believed to be characterized by a charge-transfer gap in their insulating antiferromagnetic state. The three-band Hubbard model with an on-site Cu Coulomb interaction ${\mathit{U}}_{\mathit{d}}$ , which is large compared to the difference in energy \ensuremath{\varepsilon} between the O and Cu sites, provides a basic model for such a system. We have carried out Lanczos and Monte Carlo studies of a ${\mathrm{CuO}}_{2}$ lattice described by a three-band Hubbard model. For ${\mathit{U}}_{\mathit{d}}$ large compared with \ensuremath{\varepsilon}, and \ensuremath{\varepsilon} comparable to or larger than the bandwidth of the lower hole band, we find strong antiferromagnetic correlations and evidence for a charge-transfer gap at a filling of one hole per Cu. The antiferromagnetic correlations decrease with either hole or electron doping, and we see that the additional holes go primarily on the O sites, while additional electrons go onto the Cu sites. For large values of the intersite Cu-O Coulomb interaction V, the hole-doped system exhibits a charge-transfer instability. As V is reduced, this is reflected as a peak in the charge-transfer susceptibility near \ensuremath{\varepsilon}+2V\ensuremath{\approxeq} ${\mathit{U}}_{\mathit{d}}$ , which we find is washed out by the strong Cu-O hybridization at realistic values of V. Attractive pairing interactions are found in both the d-wave and extended ${\mathit{s}}^{\mathrm{*}}$ -wave channels near the antiferromagnetic boundary.The ${\mathrm{CuO}}_{2}$ sheets common to the superconducting cuprates are believed to be characterized by a charge-transfer gap in their insulating antiferromagnetic state. The three-band Hubbard model with an on-site Cu Coulomb interaction ${\mathit{U}}_{\mathit{d}}$, which is large compared to the difference in energy \ensuremath{\varepsilon} between the O and Cu sites, provides a basic model for such a system. We have carried out Lanczos and Monte Carlo studies of a ${\mathrm{CuO}}_{2}$ lattice described by a three-band Hubbard model. For ${\mathit{U}}_{\mathit{d}}$ large compared with \ensuremath{\varepsilon}, and \ensuremath{\varepsilon} comparable to or larger than the bandwidth of the lower hole band, we find strong antiferromagnetic correlations and evidence for a charge-transfer gap at a filling of one hole per Cu. The antiferromagnetic correlations decrease with either hole or electron doping, and we see that the additional holes go primarily on the O sites, while additional electrons go onto the Cu sites. For large values of the intersite Cu-O Coulomb interaction V, the hole-doped system exhibits a charge-transfer instability. As V is reduced, this is reflected as a peak in the charge-transfer susceptibility near \ensuremath{\varepsilon}+2V\ensuremath{\approxeq}${\mathit{U}}_{\mathit{d}}$, which we find is washed out by the strong Cu-O hybridization at realistic values of V. Attractive pairing interactions are found in both the d-wave and extended ${\mathit{s}}^{\mathrm{*}}$-wave channels near the antiferromagnetic boundary.

Physical review. B, Condensed matterJul 1, 1991160 citations

Phase diagram of cuprate high-temperature superconductors based on the optimization Monte Carlo method

Takashi Yanagisawa, Masanori Miyazaki, Yamaji K.

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.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.

Modern Physics Letters BJul 3, 20202 citations

Feromagnetism in the single-band Hubbard model in the limit of strong correlations

B. M. Letfulov

Theoretical and Mathematical PhysicsDec 1, 19891 citation

A Quantum Simulation Study of Superconducting Correlation in Electron Systems with Strong Correlation

Masatoshi Imada

Quantum simulation results of superconducting correlations for strongly correlated electron systems are reported. An extended-type Hubbard model to take account of the role of oxygen sites in the CuO 2 plane of high- T c oxides is studied primarily. Superconducting susceptibility shows a tendency of quantitative enhancement at lower temperatures in contrast with the case of the single-band Hubbard model. It shows that a coupled two-band system, one with strong and the other with weak correlation, is favorable for superconductivity. A possible connection between superconducting and antiferromagnetic correlation is also discussed.Quantum simulation results of superconducting correlations for strongly correlated electron systems are reported. An extended-type Hubbard model to take account of the role of oxygen sites in the CuO 2 plane of high- T c oxides is studied primarily. Superconducting susceptibility shows a tendency of quantitative enhancement at lower temperatures in contrast with the case of the single-band Hubbard model. It shows that a coupled two-band system, one with strong and the other with weak correlation, is favorable for superconductivity. A possible connection between superconducting and antiferromagnetic correlation is also discussed.

Journal of the Physical Society of JapanSep 15, 198851 citations

On the onset of antiferromagnetism in the Hubbard model

F. Ducastelle

Physics Letters ADec 1, 19774 citations

The

{\mathrm{CuO}}_{2}

sheets common to the superconducting cuprates are believed to be characterized by a charge-transfer gap in their insulating antiferromagnetic state. The three-band Hubbard model with an on-site Cu Coulomb interaction

{\mathit{U}}_{\mathit{d}}

, which is large compared to the difference in energy \ensuremath{\varepsilon} between the O and Cu sites, provides a basic model for such a system. We have carried out Lanczos and Monte Carlo studies of a

{\mathrm{CuO}}_{2}

lattice described by a three-band Hubbard model. For

{\mathit{U}}_{\mathit{d}}

large compared with \ensuremath{\varepsilon}, and \ensuremath{\varepsilon} comparable to or larger than the bandwidth of the lower hole band, we find strong antiferromagnetic correlations and evidence for a charge-transfer gap at a filling of one hole per Cu. The antiferromagnetic correlations decrease with either hole or electron doping, and we see that the additional holes go primarily on the O sites, while additional electrons go onto the Cu sites. For large values of the intersite Cu-O Coulomb interaction V, the hole-doped system exhibits a charge-transfer instability. As V is reduced, this is reflected as a peak in the charge-transfer susceptibility near \ensuremath{\varepsilon}+2V\ensuremath{\approxeq}

{\mathit{U}}_{\mathit{d}}

, which we find is washed out by the strong Cu-O hybridization at realistic values of V. Attractive pairing interactions are found in both the d-wave and extended

{\mathit{s}}^{\mathrm{*}}

-wave channels near the antiferromagnetic boundary.