Abstract Recent discovery of high transition temperature superconductivity in La 3 Ni 2 O 7 has sparked renewed theoretical and experimental interests in unconventional superconductivity. It is crucial to understand the influence of various factors on its superconductivity. By refining the determinant quantum Monte Carlo algorithm, we characterize the parameter dependence of the superconducting transition temperature within a bilayer Hubbard model, which is sign-problem-free at arbitrary filling. A striking feature of this model is its similarity to the bilayer nickelate-based superconductor La 3 Ni 2 O 7 , where superconductivity emerges from the bilayer NiO 2 planes. We find that interlayer spin-exchange J is critical to interlayer pairing, and that on-site interaction U contributes negatively to superconductivity at low doping levels but positively at high doping levels. Our findings can provide a reference for the next step in theoretical research on nickelate-based superconductors.
Building on the recent advancements on moir\'e superlattices, we propose an exactly solvable model with Kitaev-type interactions on a bilayer honeycomb lattice for both AA stacking and moir\'e superlattices. Using Monte Carlo simulations and variational analysis, we uncover a rich variety of phases where the intra and interlayer
Z2 fluxes (visons) are arranged in a periodic fashion in the ground state, tuned by interlayer coupling and out-of-plane external magnetic field. We further extend our model to moir\'e superlattices at various commensurate twist angles around two distinct twist centers represented by
C3z and
C6z of the honeycomb lattice. Our simulations reveal generalized arrangements of plaquette values that correlate with the AA or AB stacking regions across the moir\'e unit cell. Moreover, we find that, depending on the twist angle, twist center and interlayer coupling, moir\'e superlattices exhibit to a variety of gapped and gapless spin liquid phases and can also host corner and edge modes. Our results highlight the rich physics in bilayer and twisted bilayer models of exactly solvable quantum spin liquids.
Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping ${t}_{\ensuremath{\perp}}$, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Lifshitz transition and even when it becomes incipient. Here we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing correlations in the large ${t}_{\ensuremath{\perp}}$ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased
Tc. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.