The attractive (U < 0) and repulsive (U > 0) Hubbard models have been studied using the Fermi liquid perturbation approach. The attractive Hubbard model (U < 0) is an adequate model for 3 He , an incompressible and strongly paramagnetic liquid [Formula: see text], [Formula: see text] for |U|N F = 0.9) with a pseudogap in the charge response. A pairing instability and superfluidity for U < 0 exists in the spin channel only: spin-triplet with l = 0, or spin-singlet with l = 1 (p-wave orbital state j = s + l = 1), where l is the orbital momentum of a pair. The repulsive Hubbard model (U > 0) represents a highly compressible and nearly antiferromagnetic liquid [Formula: see text], [Formula: see text] for UN F = 0.9) with a pseudogap in the spin response. However, for U > 0 a pairing instability and superconductivity exist in the charge channel only: spin-singlet with l = 0 (s-wave), or with l = 2 (d-wave) in the case of an anisotropic Fermi surface.
We have studied in terms of the effective T-matrix the self-energy part for both the attractive (U<0) and repulsive (U>0) Hubbard models. It is shown that the fluctuation pairing for strong coupling at T>T c for the attractive Hubbard model does not cause any pseudogap behavior in the single-particle density of states. We have also identified the origin of the false pseudogap for that case. Meanwhile, the fluctuation pairing significantly affect the density–density and the current–current correlation functions. As a result, there exists a pseudogap in the charge (and current) response for the attractive Hubbard model. In contrast, the pseudogap in the spin response appears to exist for the repulsive Hubbard model only. It is also shown that the contribution from the Hartree–"Cooper" channel gives an anomalous Fermi liquid term, Im χ c ≈-ω/T, to the charge response of the nearly antiferromagnetic Fermi liquid.
The paramagnetic phase of the extended attractive Hubbard model on the cubic lattice is studied within the spin rotation invariant Kotliar-Ruckenstein slave boson representation at zero temperature. It is obtained that the quasiparticle residue of the Fermi liquid phase vanishes for all densities at an interaction strength slightly smaller than [Formula: see text] that signals the Brinkman–Rice transition, and that it weakly depends on density. While for vanishing non-local interaction parameters, homogeneous static charge instabilities are found in a rather narrow window centered around quarter filling and [Formula: see text], increasing them to [Formula: see text] results into a severe narrowing of this window. On the contrary, when all interaction parameters are attractive, for example for [Formula: see text], a large parameter range in which homogeneous static charge instabilities is found. Yet, this systematically happens inside the Fermi liquid phase.
We study the possibility of a pairing instability in Fermi systems with a purely repulsive interaction potential. The effective interaction between particles at the Fermi surface is shown to contain a contribution from the fermionic background. This contribution is attractive and in many cases it overshadows the interactive potential in the pairing channels with nonzero orbital angular momenta. In particular, we show that 3D Fermi gas with repulsive interaction is unstable against p-pairing. Both the value of T c and its field dispersion are consistent with the experimental data for pure 3 He . It is also shown that in a magnetic field and in the two-band model there is the possibility of a significant mcrease of T c . We also consider the situation in two dimensions, where the effect of the fermionic background is much weaker than in the 3D case. Nevertheless, we show that the positive-U Hubbard model may have an intrinsic instability at arbitrarily small carrier densities. In particular, the Hubbard model with hopping between nearest neighbors is unstable against d-wave pairing with dxy symmetry of the gap wave function. The superconducting states we study correspond to the actual minima of the Free energy.
The search for superconductivity with unconventional pairing symmetry has been a central focus in the study of strongly correlated electron systems. In this work, we report a numerically exact study of the spin-triplet pairing in a two-dimensional Hubbard model with repulsive interactions, employing the determinant quantum Monte Carlo method. The model includes next-nearest-neighbor and third-nearest-neighbor hopping terms and maintains spin balance. By tuning the fermion filling close to a type-II Van Hove singularity (VHS) in the model, we numerically investigate the ordering tendencies of several possible pairing channels with different symmetries. Our numerical results provide clear evidence of the spin-triplet
p-wave pairing instability approaching low temperatures, as revealed by the vertex contribution to the pairing susceptibility. This signature becomes increasingly pronounced as the interaction strength increases in the weak to intermediate regime. We further find that, near the type-II VHS, the dominant spin-spin correlations in the system are ferromagnetic, suggesting its close relation to the spin-triplet pairing instability. Our findings offer a reliable approach to realize spin-triplet
p-wave superfluidity in the repulsive Hubbard model from an unbiased numerical perspective.
The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while
B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) and
B2g (
dxy) pairing dominates in the absence of repulsive longer-range Coulomb interactions
VNN, the latter induces pairing in other symmetry channels, including, e.g.,
A2g (
g-wave), nodal
A1g (extended
s-wave), or nodal
Eu (
p-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction,
VNN<0, on the superconducting gap structure. Depending on the electronic filling, such an attraction boosts
Eu (
p-wave) spin-triplet or
B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) spin-singlet ordering.
We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely, a Mott insulator in the paramagnetic and antiferromagnetic phases, and a putative
d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultracold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We argue that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are easier to observe in the attractive Hubbard mode as a band insulator of Cooper pairs and superfluid phase, respectively. The putative
d-wave superfluid phase of the repulsive Hubbard model doped away from half filling is related to a
d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to ``quantum simulate'' the Hubbard model in an optical lattice over the simulation of the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.