Repulsive Hubbard Model Research Articles

Higher Order Perturbation Expansion for Pairing Interaction in Repulsive Hubbard Model

We calculate the effective pairing interaction in the Hubbard model on the two-dimensional square lattice, by applying perturbation expansion up to the fourth order in the on-site repulsion U . We evaluate transition temperature as functions of the repulsion U . We consider only the following two typical cases (I) and (II): (I) The system is near the half-filled state, and the Fermi surface nesting yields the strong antiferromagnetic fluctuations. (II) The system is away from the half-filled state. This case is intended to reproduce the single main band of the spin–triplet superconductor Sr 2 RuO 4 . In the both cases, the Fermi level is set close to the Van Hove singularity. In the case (I), each order of the perturbation expansion for the pairing interaction gives a similar momentum dependence, and in addition the perturbation expansion for the pairing interaction converges relatively well even for moderately strong U . On the other hand, in the case (II), the perturbation expansion does not converge we...

Superconductivity in repulsive electron systems with three-dimensional disconnected Fermi surfaces

The idea of raising Tc in the spin-fluctuation mediated superconductivity on disconnected Fermi surfaces with the gap function changing sign across but not within the Fermi pockets, proposed by Kuroki and Arita for two dimensions (2D), is here extended to three-dimensional (3D) systems. Two typical cases of 3D disconnected Fermi surfaces (stacked bond-alternating lattice and stacked ladder layers) are considered. By solving Eliashberg's equation for Green's function obtained with the fluctuation exchange approximation (FLEX) for the repulsive Hubbard model on these structures, we have shown that Tc can indeed reach O(0.01t), which is almost an order of magnitude higher than in ordinary 3D cases and similar to those for the best case found in 2D. The key factor found here for the favorable condition for the superconductivity on disconnected Fermi surfaces is that the system should be quasi-low dimensional, and the peak in the spin susceptibility should be appropriately "blurred".

Delocalizing effect of the Hubbard repulsion for electrons on a two-dimensional disordered lattice

We study numerically the ground-state properties of the repulsive Hubbard model for spin-1/2 electrons on two-dimensional lattices with disordered on-site energies. The projector quantum Monte Carlo method is used to obtain very accurate values of the ground-state charge density distributions with $N_p$ and $N_p+1$ particles. The difference in these charge densities allows us to study the localization properties of an added particle. The results obtained at quarter-filling on finite clusters show that the Hubbard repulsion has a strong delocalizing effect on the electrons in disordered 2D lattices. However, numerical restrictions do not allow us to reach a definite conclusion about the existence of a metal-insulator transition in the thermodynamic limit in two-dimensions.

Flow of the quasiparticle weight in theN-patch renormalization group scheme

Using the N-patch renormalization group method we investigate the flow of the quasiparticle weight in one-dimensional, weakly two-dimensional and fully two-dimensional Hubbard models. In one dimension we reproduce the Luttinger exponent that describes the disappearance of the quasiparticle peak towards lower scales. Further we analyze effects of the band structure, interchain hopping and the flow of the interactions in quasi-one-dimensional models. For the two-dimensional case we study how the suppression of the quasiparticle weight affects the flow to strong coupling. We find that the flow to strong coupling remains essentially unchanged. This strengthens the evidence for d-wave superconductivity in the weakly repulsive Hubbard model.

INTERPLANAR HOPPING OF W = 0 BOUND PAIRS

CuO 4 is the simplest of a class of repulsive Hubbard model clusters which (under well specified conditions) display W = 0 pairing; remarkably, ane also observes superconducting quantization of a magnetic flux orthogonal to the plane. Thus one can use CuO 4 units connected by weak O-O and/or Cu-Cu links to model interplanar coupling and c-axis superconductivity in Cuprates. A new analytic approximation supported by preliminary numerical evidence suggests that in such models one can study the propagation of bound pairs and also the superconducting flux quantization in a 3d geometry.

Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model

Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the noninteracting) Hamiltonian. We describe such a renormalized perturbation expansion for interacting Fermi systems, which treats Fermi surface shifts and superconductivity with an arbitrary gap function via additive counterterms. The expansion is formulated explicitly for the Hubbard model to second order in the interaction. Numerical solutions of the self-consistency condition determining the Fermi surface and the gap function are calculated for the two-dimensional case. For the repulsive Hubbard model close to half-filling we find a superconducting state with d-wave symmetry, as expected. For Fermi levels close to the van Hove singularity a Pomeranchuk instability leads to Fermi surfaces with a broken square lattice symmetry, whose topology can be closed or open. For the attractive Hubbard model the second-order calculation yields an s-wave superconductivity with a weakly momentum dependent gap, whose size is reduced compared to the mean-field result.

Superconductivity induced by interband nesting in the three-dimensional honeycomb lattice

In order to study whether the interband nesting can favor superconductivity arising from electron-electron repulsion in a three-dimensional system, we have looked at the repulsive Hubbard model on a stack of honeycomb (i.e., non-Bravais) lattices with the fluctuation exchange approximation, partly motivated by the superconductivity observed in ${\mathrm{MgB}}_{2}.$ By systematically changing the shape of Fermi surface with varied band filling n and the third-direction hopping, we have found that the pair scattering across the two bands is indeed found to give rise to gap functions that change sign across the bands and behave as an s or d wave within each band. This implies (a) the electron repulsion can assist gapful pairing when a phonon-mechanism pairing exists and (b) the electron repulsion alone, when strong enough, can give rise to a d-wave-like pairing, which should be, for a group-theoretic reason, a time-reversal broken $d+id$ with point nodes in the gap.

Theory of electrical transport in the pseudogap state: effects of spin fluctuations and superconducting fluctuations

Electrical transport in High- T c superconductors is investigated. The main interest is on the pseudogap state, which is induced by the superconducting (SC) fluctuations. The electric transport shows a characteristic behavior in the pseudogap state, which is considerably different from the magnetic and single-particle properties. We show that these properties are comprehensively explained by taking into account the spin fluctuations and SC fluctuations simultaneously. It is pointed out that the characteristic momentum dependences of the system play an essential role in this explanation. We perform the microscopic calculation to describe the SC fluctuations and pseudogap phenomena, starting from the repulsive Hubbard model. This is the self-consistent FLEX+ T-matrix approximation in which the spin fluctuations, SC fluctuations and their effects on the single-particle self-energy are determined self-consistently. The longitudinal and transverse conductivities are calculated by using the Éliashberg and Kohno–Yamada formalism. The in-plane and c-axis optical conductivities are also calculated. The effects of the spin fluctuations and SC fluctuations are estimated, respectively. The results clarify the main effect of the SC fluctuations on the transport coefficients and give a consistent understanding with the experimental results.

Third-order perturbation analysis for p- and d-wave pairing states in two-dimensional repulsive Hubbard model

We study instability of a singlet and triplet pairing states in a quasi-two-dimensional Hubbard model on the basis of the third-order perturbation theory. Comparing the result obtained here with that is obtained by using only the second-order effective interaction, a stable p-wave state spreads from low to intermediate density region. The vertex correction of the third-order effective interaction makes a d x 2− y 2 -wave state for the high density near half-filling. On the other hand, the third-order term makes the p-wave state dominant.

Magnetic properties of the infinitely repulsive Hubbard model near half filling

Many theoretical works discuss the magnetic properties of the strongly repulsive Hubbard model near half filling. Several authors suggest that the system which contains a few holes does not behave as a ferromagnet, unlike in the one-hole case described by Nagaoka's famous result. We discuss the finite temperature properties of finite lattices. Using an efficient Monte Carlo method magnetic and specific heat results are presented for a 10 by 10 lattice with two holes. Our results show that the magnetization increases with decreasing temperature for such a finite system.

Superconductivity, Magnetism and Mapping between the Attractive and Repulsive Hubbard Models

The exact Bethe-ansatz and generalized self-consistent field (GSCF) ground-state properties of the one-dimensional (1d) Hubbard model for U >0 and U 0 and U <0 models.

Phase Diagram and Magnetic Correlations in One-Dimensional Repulsive Hubbard Model with Magnetic Field

The generalized self-consistent field (GSCF) theory for the one-dimensional repulsive Hubbard model at half-filling is examined in the presence of magnetic field h in wide range of interaction strength U / t . The evolution of the energy gap in the presence of magnetc field describes a magnetic crossover from itinerant magnetism of weakly bound electron-hole pairs with k F =π/2 to the localized magnetic regime, with the Bose condensation of local electron-hole pairs ( k F =0).

Nearest-neighbor attraction stabilizes staggered currents in the two-dimensional Hubbard model

Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive two-dimensional Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbor repulsions are present. However, staggered flux ordering emerges when attractive nearest-neighbor Coulomb interactions are included. Such ordering opens a gap along the $(\ensuremath{\pi},0)\ensuremath{-}(0,\ensuremath{\pi})$ direction and persists over a reasonable range of doping.

Theory of Electric Transport in the Pseudogap State of High-Tc Cuprates

We theoretically investigate the electric transport in the pseudogap state of High-Tc cuprates. Starting from the repulsive Hubbard model, we perform the microscopic calculation to describe the pseudogap phenomena which are induced by the superconducting fluctuations. The single particle Green function, spin susceptibility and superconducting fluctuations are self-consistently determined by the SC-FLEX+T-matrix approximation. The longitudinal and transverse conductivities are calculated by using the Eliashberg and Kohno-Yamada formalism. The effects of the spin fluctuations and superconducting fluctuations are estimated, respectively. The vertex corrections arising from the two fluctuations are also calculated. The additional contribution from the Aslamazov-Larkin term is also estimated beyond the Eliashberg formalism. It is shown that the main effect of the superconducting fluctuations is the feedback effect through the spin fluctuations. The correct results are obtained by considering the superconducting fluctuations and the spin fluctuations simultaneously. The temperature and doping dependences of the resistivity and the Hall coefficient are well explained. We point out that the characteristic momentum dependence of the systems plays an essential role in this explanation.

Constrained-path quantum Monte Carlo simulations of the zero-temperature disordered two-dimensional Hubbard model

We study the effects of disorder on long-range antiferromagnetic correlations in the half-filled, two-dimensional, repulsive Hubbard model at $T=0.$ A mean field approach is first employed to gain a qualitative picture of the physics and to guide our choice for a trial wave function in a constrained path quantum Monte Carlo (CPQMC) method that allows for a more accurate treatment of correlations. Within the mean field calculation, we observe both Anderson and Mott insulating antiferromagnetic phases. There are transitions to a paramagnet only for relatively weak coupling, $U&lt;2t$ in the case of bond disorder, and $U&lt;4t$ in the case of on-site disorder. Using ground-state CPQMC we demonstrate that this mean field approach significantly overestimates magnetic order. For $U=4t,$ we find a critical bond disorder of ${V}_{c}\ensuremath{\approx}(1.6\ifmmode\pm\else\textpm\fi{}0.4)t$ even though within mean field theory no paramagnetic phase is found for this value of the interaction. In the site disordered case, we find a critical disorder of ${V}_{c}\ensuremath{\approx}(5.0\ifmmode\pm\else\textpm\fi{}0.5)t$ at $U=4t.$

The U = ∞ Hubbard model with few holes: Monte Carlo studies near half-filling at non-zero temperatures

We present an efficient Monte Carlo method to study the properties of the infinitely repulsive Hubbard model with few holes at finite nonzero temperatures. Using this method, magnetic and specific heat results are presented for a 10 by 10 lattice with two holes. Our results show that the magnetization increases with decreasing temperature for such a finite system.

Study of Superconductivity in Borocarbides on the Basis of Perturbation Theory

The borocarbide YNi 2 B 2 C with quasi-2-dimensional structure encounters a superconducting transition at T c = 15.4 K, the pairing symmetry of which is not clarified; most of experiments suggest an extended s -wave state, while some claim a d -wave. In this paper, we investigate a possibility of a d -wave state, solving the Eliashberg equation within the third order perturbation theory for a repulsive Hubbard model with the band structure reproducing the main Fermi surface. It is shown that if the electron correlation gives the dominant contribution to the superconducting pairing interaction, the d x y -symmetry is the most favorable state corresponding to the (π, 0) peak structure of the spin susceptibility.

Perturbation Analysis of Pairing Symmetry and Transition Temperature in Quasi-One-Dimensional Organic Superconductors

We investigate pairing symmetry in quasi-one-dimensional organic superconductors, solving Eliashberg's equation within third order perturbation theory for a repulsive Hubbard model. According to the calculation results, spin-singlet state is expected to give higher transition temperature than spin-triplet one and the vertex corrections reduce the transition temperature for the spin-singlet case. It is shown that the contributions of antiferromagnetic spin fluctuations dominate strongly the momentum dependence of the effective pairing interaction for both of the spin-triplet and the spin-singlet pairing cases.

Quantum Monte Carlo simulation of the triangular lattice in the repulsive Hubbard model

The repulsive Hubbard model for the triangular lattice in two dimensions is studied by means of a quantum Monte Carlo simulation in the grand canonical ensemble. Both on-site and nearest neighbor Coulomb interactions are taken into account. The one-electron spectral function A(kω) is shown to gradually develop a gap as the temperature is lowered provided the Hubbard U is larger than the bandwidth. Analysis of the spin and charge structure factors (static correlation functions) shows that, while the charge factor remains featureless, the spin factor develops a strong peak very close to the M′ point (2π/3,0) of the small surface Brillouin zone (corresponding to the three-sublattice model). Implications for the behavior of the 3×3 adlayer structures on fourth-group semiconductor surfaces are briefly commented upon.

Spin-triplet superconductivity in repulsive Hubbard models with disconnected Fermi surfaces: A case study on triangular and honeycomb lattices

We propose that spin-fluctuation-mediated spin-triplet superconductivity may be realized in repulsive Hubbard models with disconnected Fermi surfaces. The idea is confirmed for Hubbard models on triangular (dilute band filling) and honeycomb (near half-filling) lattices using fluctuation exchange approximation, where triplet pairing order parameter with f-wave symmetry is obtained. Possible relevance to real superconductors is suggested.