Single-band Hubbard model with spin-orbit coupling

A single-band Hubbard hamiltonian with spin-orbit coupling included in the hopping integral is solved in terms of the solution with no spin-orbit coupling. For an openended linear chain the spectrum is independent ofu/t=tan θ, whereu(t) measures the spin-orbit (ordinary) contribution to the hopping integral; and for the half-filled band the spin-correlations are spiral-like with turn angle 2θ+π. In the case of a ring ofN sites the spectrum is periodic in θ with period 2π/N; for the half-filled-band case the period is π/N in the zero-band-width limit. Generalizations to higher dimensions are noted.     

Evidence for d-wave superconductivity in the repulsive Hubbard model

We perform numerical simulations of the Hubbard model using the projector Quantum Monte Carlo method. A novel approach for finite size scaling is discussed. We obtain evidence in favor of d-wave superconductivity in the repulsive Hubbard model. For U=4, is roughly estimated as K. Received 8 September 1998     

Strong coupling Hubbard model and superconductivity

We have shown that systems open to fermion number fluctuations and described by the Hubbard model can be superconducting. This superconductivity must be accompanied by a special type of magnetic order. A unitary transformation is explicitly constructed by which the large interaction term of the Hubbard model is exactly diagonalized. Order parameters of the system related to Green functions of fermions are explicitly evaluated in the strong coupling limit. This model applied to copper-oxygen chains provides a theoretical explanation of highT _c superconductivity in compounds of the type YBa₂Cu₃O_7–x .Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Odd-frequency superconductivity on quasi-one-dimensional triangular lattice in the Hubbard model

We study the superconductivity in the Hubbard model on quasi-one-dimensional triangular lattice using random phase approximation (RPA). We find that odd-frequency spin-singlet p-wave pairing can be realized on isosceles quasi-one-dimensional triangular lattice.     

Odd-frequency superconductivity on the Hubbard model using the FLEX approximation

It is an important issue to clarify whether the odd-frequency superconducting state can be derived from microscopic Hamiltonian or not, where gap function has an odd-parity in frequency. We study the instability of following four superconducting states: (1) even-frequency spin-singlet, (2) even-frequency spin-triplet, (3) odd-frequency spin-singlet and (4) odd-frequency spin-triplet. By using the fluctuation exchange (FLEX) approximation on a triangular and square lattice, we find that the odd-frequency spin-triplet pairing can become dominant at a certain region where the suppression of the antiferromagnetic fluctuation due to a geometric frustration becomes prominent.     

d x 2 - y 2 superconductivity and the Hubbard model

The numerical studies of d x 2 - y 2 -wave pairing in the two-dimensional (2D) and the 2-leg Hubbard models are reviewed. For this purpose, the results obtained from the determinantal Quantum Monte Carlo and the Density-Matrix Renormalization-Group calculations are presented. These are calculations which were motivated by the discovery of the high- T c cuprates. In this review, the emphasis is placed on the microscopic many-body processes which are responsible for the d x 2 - y 2 -wave pairing correlations observed in the 2D and the 2-leg Hubbard models. In order to gain insight into these processes, the results on the effective pairing interaction as well as the magnetic, density and the single-particle excitations will be reviewed. In addition, comparisons will be made with the other numerical approaches to the Hubbard model and the numerical results on the t - J model. The results reviewed here indicate that an effective pairing interaction which is repulsive at ( ~ , ~ ) momentum transfer, and enhanced single-particle spectral weight near the ( ~ ,0) and (0, ~ ) points of the Brillouin zone, create optimum conditions for d x 2 - y 2 -wave pairing. These are two effects which act to enhance the d x 2 - y 2 -wave pairing correlations in the Hubbard model. Finding additional ways is an active research problem.     

Monte-Carlo algorithm for a two-dimensional Hubbard model of high-T c superconductivity

A Monte-Carlo procedure is given for the two-dimensional (2-D) Hubbard model using the Suzuki-Trotter transformation. The resulting three-dimensional (3-D) classical model does not have the usual problems with negative transition probabilities in the large-U limit (U-repulsive interactions). Numerical simulations based on the algorithm described are expected to be of importance for the theory of high-T _c superconductivity.