We investigate the finite temperature properties of the extended Hubbard model with a nearest-neighbor Coulomb repulsion on the square lattice. Solving the self-consistent equations obtained using our mean-field theory [J. Phys. Soc. Jpn. 88, 084706 (2019)] numerically, we obtain three-dimensional phase diagrams of the (d_{x^{2} - y^{2}})-density wave (DDW) and (d_{x^{2} - y^{2}})-wave superconducting (DSC) order parameters according to temperature and hole concentrations. The obtained phase diagrams show three distinctive regions: underdoped, optimal, and overdoped. Within the underdoped region, the ratios of the order parameters at absolute zero temperature to the critical temperatures are in approximate agreement with the experimental results of cuprate high Tc superconductors. The optimal region exhibits a unique reentrant phenomenon regarding the hole concentration. In the overdoped region, the DDW disappears and the DSC becomes normal.
We show in a mean-field calculation that phase diagrams remarkably similar to those recently proposed for the cuprates arise in simple microscopic models of interacting electrons near half-filling. The models are extended Hubbard models with nearest-neighbor interaction and correlated hopping. The underdoped region of the phase diagram features ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ density-wave (DDW) order. In a certain regime of temperature and doping, DDW order coexists with antiferromagnetic order. For larger doping, it coexists with ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity. While phase diagrams of this form are robust, they are not inevitable. For other reasonable values of the coupling constants, drastically different phase diagrams are obtained. We comment on implications for the cuprates.
We study the square-lattice extended Hubbard model with on-site
U and nearest-neighbor
V interactions by exact diagonalization. We show that nonequilibrium quench dynamics can help determine the equilibrium phase transition boundaries, which agree with the calculations of the fidelity metric, dynamical structure factor, and correlation function. At half filling, the phase diagrams in the strong-coupling regime include spin density wave and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductivity at large positive
U, charge density wave (extended
s∗-wave superconductivity) at large positive (negative)
V, and
s-wave superconductivity at large negative
U with vanishing
V. The energies of different particle sectors also help determine the phase separation region. With carrier doping, charge fluctuation results in a strong competition between different orders, making it more difficult to identify the leading instability on finite-size clusters. Nevertheless, the more exotic
p-wave superconducting pairing is found to be enhanced when the system is heavily overdoped by
37.5 holes, especially in the interaction parameter range relevant to the cuprate superconductors.
We consider various incommensurate (IC) order parameters for electrons on a square lattice which reduce to
dx2−y2-density wave (DDW) order when the ordering wavevector
Q→(π,π). We describe the associated charge and current distributions and their experimental signatures. Such orders can arise at the mean-field level in extended Hubbard models. We compare the phase diagrams of these models with experiments in the underdoped cuprates, where (1) DDW order is a possible explanation of the pseudogap, and (2) there are experimental indications of incommensurability. We find various types of IC DDW and discuss their possible relevance to the physics of the cuprates. Our main finding is that IC DDW order is generally accompanied by superconducting order, but the magnitude of the IC wavevector can be small. A comparison with the analogous AF-ICSDW transition is given.
The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.
The two-dimensional (2D) Hubbard model is widely believed to contain the key ingredients of high-temperature superconductivity in cuprate materials. Here, we report a constrained path quantum Monte Carlo (CPQMC) study of the square-lattice extended Hubbard model with on-site Coulomb repulsion U and nearest-neighbor (NN) electron attraction V. Upon doping
δ= 0.125, we find that the NN electron attraction V can notably drive an exotic spin-triplet (p-wave) superconducting (SC) phase, and enhance the p-wave SC correlations with the increase of V. But in the intermediate coupling regime, the
dx2−y2-wave (d-wave) does not significantly increase with the increase of V, indicating that the d-wave is not affected by V in strongly correlated system. Besides the pairing phase, a spin density wave (SDW) only exists near the half-filling in the particle-hole channel, and doping disrupts the formation of SDW order. Especially, the NN electron attraction V has no significant effect on SDW, reflecting the consistent relationship between d-wave SC and spin correlation. Moreover, as doping increases, the dominant region of p-wave also expands, further suppressing the presence of d-wave, which may help explain the disappearance of d-wave SC in overdoped cuprate superconductors. We also find the d-wave exhibits a singular nonzero (near point (
2π/3,π)) condensation structure in momentum space, resulting in a different staggered behavior in the x and y direction with distance in real space. On the contrary, the p-wave condensed at zero momentum, and the p-wave correlation exhibits exponential decay in real space. Our work suggests the p-wave SC region can be induced and further broadened by the NN electron attraction V, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate materials.
We study an extended Hubbard model with on-site repulsion and nearest-neighbors attraction which tries to mimic some of the experimental features of doped cuprates in the superconducting state. We draw and discuss the phase diagram as a function of the effective interactions among electrons for a wide range of doping concentrations. We locate the region which is relevant for the cuprates setting some constraints on the parameters which may be used in this kind of effective model. We also study the effects of temperature and orthorombicity on the symmetry and magnitude of the gap function, and map the model onto a simpler linearized Hamiltonian, which produces similar phase diagrams.