Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO
2 planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two-dimensional Hubbard Hamiltonian. In this paper, we use determinant quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the
d-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearance of more nearly half-filled regions when the doped holes are confined to the stripes. We also observe a $\ensuremath{\pi}$-phase shift in the magnetic order.
The two-dimensional Hubbard model is widely believed to capture the key ingredients of high-temperature superconductivity in cuprate materials. Here we report a constrained path quantum Monte Carlo study of the square-lattice extended Hubbard model with on-site Coulomb repulsion
U and nearest-neighbor (NN) electron attraction
V. Upon doping $\ensuremath{\delta}$ = 0.125, we find that NN electron attraction
V significantly promotes an exotic spin-triplet (
p-wave) pairing, with the
p-wave pairing correlations growing stronger as
V increases. Meanwhile, the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave (
d-wave) pairing in the intermediate coupling regime shows an insignificant response to the increase of
V. The spin density wave order, which is observed near half filling in the particle-hole channel, is also almost unaffected by the NN electron attraction
V, reinforcing the established relationship between
d-wave superconductivity (SC) and spin order. As the doping becomes heavier (i.e., $\ensuremath{\delta}$ increases), the dominant region of
p-wave pairing expands, further suppressing the presence of
d-wave pairing. Our paper suggests the
p-wave pairing region can be induced and further broadened by the NN electron attraction
V, offering a feasible mechanism to realize
p-wave SC in realistic cuprate materials.
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.
D-wave superconductivity in high-Tc cuprates is believed to be strongly intertwined with stripe order. In this work, using the constrained-path quantum Monte Carlo method, we study the superconducting behavior of a dimer-embedded extended Hubbard model with on-site repulsion U and nearest-neighbor attractive interaction V. Our results show that when the hopping between the dimer and its surroundings is small and U is less than
2.0,V induces a significant enhancement of d-wave superconductivity, mainly contributed by partially filled stripes consisting of one-dimensionally arranged dimers. This work provides a new platform for a deeper understanding of the interplay between d-wave superconductivity and stripe order in high-Tc cuprates.
Abstract D -wave superconductivity in high- T c cuprates is believed to be strongly intertwined with stripe order. In this work, using the constrained-path quantum Monte Carlo method, we study the superconducting behavior of a dimer-embedded extended Hubbard model with on-site repulsion U and nearest-neighbor attractive interaction V . Our results show that when the hopping between the dimer and its surroundings is small and U is less than induces a significant enhancement of d -wave superconductivity, mainly contributed by partially filled stripes consisting of one-dimensionally arranged dimers. This work provides a new platform for a deeper understanding of the interplay between d -wave superconductivity and stripe order in high- T c cuprates.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near
1/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about
1/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.