The Hubbard model is known to accommodate various electronic orders, including stripes, which are important for understanding the physics of cuprates. We study spin-stripe order in the square lattice Hubbard model as a function of doping and temperature, by solving the Bethe-Salpeter equation with the local vertex from dynamical mean field theory (DMFT), both inside and outside the antiferromagnetic phase. We find broad regions of horizontal/vertical spin stripes at low temperatures for the model with and without next-nearest neighbor hopping. Their wavelength depends on hole doping in a nonlinear fashion, and is highly sensitive to the ratio of nearest and next-nearest neighbor hoppings.
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 three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an ``optimal'' value of the charge-transfer energy for the model where
Tc is largest. These results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.
As a model for high-
Tc superconductors, a two-band Hubbard model is proposed. When the Coulomb interactions are introduced between the \ensuremath{\alpha} and \ensuremath{\beta} orbitals, an effective attraction of carriers in the \ensuremath{\beta} (doped) band is shown to arise in an appropriate condition. The quantum Monte Carlo method is used to confirm the occurrence of Cooper pairing in finite two-band Hubbard systems. The attraction, which also appears in the density-density correlation, enhances the on-site singlet Cooper pair-pair correlation in the \ensuremath{\beta} band and suppresses the antiferromagnetic spin-spin correlation in the \ensuremath{\alpha} band. The criterion for the pairing and the nature of the pairing are discussed. Thus we provide a mechanism of superconductivity specific to strongly correlated two-band systems.
In this thesis, we tackle various problems in strongly correlated electron systems, which can be addressed properly via the non-perturbative dynamical mean field theory (DMFT) approach using the continuous time quantum Monte Carlo method as an impurity solver. First, we revisit the old Nagaoka ferromagnetism problem in the U=oo Hubbard model and study the stability of the ferromagnetic state as a function of the temperature, the doping level, and the next-nearest-neighbor hopping t'. We then address the nature of the Mott transition in the two-dimensional Hubbard model at half-filling using cluster DMFT. Cluster DMFT can incorporate the short-range correlations beyond DMFT by extending the spatial range in which correlations are treated exactly to a finite cluster size. The non-local correlations reduce substantially the critical interaction U and modify the shape of the transition lines in the phase diagram. We then concentrate on the calculation of two-particle response functions from the ab initio perspective by means of computing the one-particle excitation spectrum using the combination of the density functional theory (DFT) and DMFT and extracting the two-particle irreducible vertex function from a local two-particle Green's function computed within DMFT. In particular, we derive the equations for calculating the magnetic/charge susceptibility and the pairing susceptibility in superconductivity. This approach is applied to the Hubbard model and the periodic Anderson model and we determine the phase diagram of magnetism and superconductivity in these models. We show that the superconducting phase is indeed stable near the magnetic phase where the pairing interaction mediated by spin fluctuations is dominantly enhanced. The non-local correlation effect to superconductivity is also discussed using the dual fermion approach and the dynamical vertex approximation. We finally apply the vertex function approach within DFT+DMFT to a Fe-based superconductor, BaFe2As2, and compute the dynamical magnetic susceptibility in this material. Our calculation results show a good agreement with the magnetic excitation spectra observed in a neutron scattering experiment. The response function calculation method derived in this thesis can capture both a localized and an itinerant nature of collective excitations in strongly correlated electron systems.
The nearest-neighbor superexchange-mediated mechanism for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion
U=9t and nearest-neighbor repulsion
V=0,2t,4t. In the underdoped regime,
V increases the CDMFT superconducting transition temperature
Tcd even though it decreases the superconducting order parameter at low temperature for all dopings. However, in the overdoped regime
V decreases
Tcd. We gain insight into these paradoxical results through a detailed study of the frequency dependence of the anomalous spectral function, extracted at finite temperature via the MaxEntAux method for analytic continuation. A systematic study of dynamical positive and negative contributions to pairing reveals that even though
V has a high-frequency depairing contribution, it also has a low frequency pairing contribution since it can reinforce superexchange through $J=4{t}^{2}/(U\ensuremath{-}V)$. Retardation is thus crucial to understanding pairing in doped Mott insulators, as suggested by previous zero-temperature studies. We also comment on the tendency to charge order for large
V and on the persistence of
d-wave superconductivity over extended-
s or
s+d wave.