We perform a renormalized mean-field study of the two-dimensional repulsive Hubbard model, focusing on the intricate interplay and possible coexistence of magnetic, charge, and superconducting orders. We improve on conventional mean-field theory by utilizing a renormalization group framework that captures high-energy fluctuations. This method generates effective magnetic and d -wave pairing interactions, and allows for an unbiased exploration of coexisting phases at weak and moderate interaction strengths. Unrestricted mean-field calculations of the effective Hamiltonian on large finite lattices are combined with analyses in the thermodynamic limit, revealing a rich phase diagram with extensive regions of coexisting orders. We find that d -wave superconductivity coexists with Néel order on the electron-doped side. On the hole-doped side, superconductivity is found to coexist with spiral or stripe magnetic orders. Within the stripe-ordered region, the superconducting order parameter is spatially modulated, with a period that follows the charge modulation of the stripes. Below Van Hove filling, pairing provides the primary energy gain, while the stripe order yields only a small, and hence fragile, additional energy lowering.
In this work we have considered a two-dimensional two-band Hubbard model (extended Hubbard model) to study the effect of the nonlocal hybridization
Vk on the superconductivity. In the strong-coupling regime and for a
d-wave superconducting gap, we have obtained the superconducting critical temperature
Tc and the zero-temperature superconducting gap ${\ensuremath{\Delta}}_{0}$ for different hybridizations. We have adopted hopping parameters suitable to describe the high-temperature superconductor materials. The results show that for a fixed value of the hybridization and the intraband $d\text{\ensuremath{-}}d$ attractive potential
U, the gap increases for low temperatures and diminishes as the temperatures increase toward
Tc. As the hybridization increases both, ${\ensuremath{\Delta}}_{0}$ and
Tc, diminish. For each hybridization, the quantity $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}$ increases and saturates in a particular value as
U increases. The relation between applied pressure
P and hybridization in the strong-coupling regime is also discussed.
To understand the interplay of d-wave superconductivity and antiferromagnetism, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. The Hamiltonian is solved in the mean field approximation on a finite lattice. In the impurity-free case, the minimum energy solutions show phase separation as predicted previously based on free energy argument. The phase separation tendency implies that the system can be easily rendered inhomogeneous by a small external perturbation. Explicit solutions of a model including weak impurity potentials are indeed inhomogeneous in the spin-density-wave and d-wave pairing order parameters. Relevance of the results to the inhomogeneous cuprate superconductors is discussed.
We present an approach to investigate the interplay of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model within a numerically exact cluster dynamical mean-field approximation. Self-consistent solutions with two nonzero order parameters exist in a wide range of doping level and temperatures. A linearized equation for the energy spectrum near the Fermi level has been solved. The resulting d-wave gap has the correct magnitude and k dependence, but some distortion compared to the pure ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting order parameter due to the presence of underlying antiferromagnetic ordering.
We use cellular dynamical mean-field theory with extended unit cells to study the ground state of the two-dimensional repulsive Hubbard model at finite doping. We calculate the energy of states where
d-wave superconductivity coexists with spatially nonuniform magnetic and charge order and find that they are energetically favored in a large doping region as compared to the uniform solution. We also study the spatial form of the density and the superconducting and magnetic order parameters at different doping values.