We have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first- and second-neighbor hopping terms in order to study the coexistence state of a static stripe state and a modulated d-wave superconductivity in the underdoped cuprates. In addition to a Gutzwiller, a Jastrow and a doublon-holon correlation effects, the band-renormalization effect was considered in the trial wave function. The condensation energies of an 8-period stripe state was computed as a function of a Coulomb energy under the hole-density x=1/8. Our results reveal that the renormalization of higher hopping parameters due to the strong correlation effect enhances the one-dimensional hole motion on a quarter-filled band in the stripe state, and brings quasi-Fermi surface close to the magnetic zone boundary in the coexistence state.
In order to study the material dependence of the correlation between stripes and dx2-y2-wave superconductivity (SC) among cuprate superconductors, we have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first-, second- and third-nearest-neighbor hopping terms (t, t’ and t”, respectively) by using the Gutzwiller-Jastrow-type wave function taking account of three-body correlations on a triangle, which is efficient for frustrated systems. The condensation energies of the vertical stripes and the homogeneous SC were computed as a function of t’/t with a fixed relation t”= –t’/2. We have found that, at the nearly optimal doping with moderately strong on-site Coulomb interaction, the state of maximum condensation energy switches from the vertical stripes to the homogeneous dSC as |t’/t| increases.
We study the competition between stripe states with different periods and a uniform
d-wave superconducting state in the extended two-dimensional Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping ${t}^{\ensuremath{'}}$, the preferred period of the stripe decreases. For the values of ${t}^{\ensuremath{'}}$ predicted for cuprate high-
Tc superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at
1/8 doping. Only at larger doping, $0.18\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, the period 4 stripe exhibits coexisting
d-wave superconducting order. The uniform
d-wave state is only favored for sufficiently large positive ${t}^{\ensuremath{'}}$.