This work investigates the exciton property of the bilayer Hubbard model by using the con- strained-path Monte Carlo method. The calculated results show that when the doping density is lower than 0.08, the local exciton characterized by interlayer single particle tunneling is enhanced by the interlayer Coulomb interaction V, and the enhancement becomes stronger with decreasing the doping density. However, when the doping density is higher than 0.08, the local exciton is sup- pressed by V. This result exhibits significant differences from the published results at finite tem- peratures. Further analysis shows that the long-range exciton correlation function is reduced with increasing V, demonstrating that there does not exist exciton condensation in the studied model. In addition, the interlayer Coulomb interaction V is shown to have a rather weak effect on local magnetic moment.
We studied the possibility of exciton condensation in a strongly correlated bilayer extended Hubbard model using determinant quantum Monte Carlo. To model both the on-site repulsion
U and the interlayer interaction
V we introduced an update scheme extending the standard Sherman-Morrison update. We observe that the sign problem increases dramatically with the inclusion of the interlayer interaction
V, which prohibits at this stage an unequivocal conclusion regarding the presence of exciton condensation. However, enhancement of the interlayer tunneling results suggest that the strongest exciton condensation tendency lies around
10−−20 p/
n doping. Magnetic properties and conductivity turn out to be relatively independent of the interlayer interaction.
The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and interlayer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π,π) charge density wave state. We extract the Berezinskii-Kosterlitz-Thouless transition temperature from superfluid density and a finite-size scaling analysis of the correlation functions and explain our results in terms of an effective biexcitonic hard-core boson model.
The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher-
Tc superconductors. In particular, the relationship between the number
n of CuO
2 layers in a unit cell of cuprate superconductors and the optimum superconducting transition temperature
Tcopt is intriguing. As experimentally observed in layered cuprates,
Tcopt increases when
n is increased, up to
n=3, and, then, decreases for larger
n. However, the mechanism behind the
n dependence of
Tcopt remains elusive although there have been many studies on the
n dependence. In this paper, we studied a bilayer
t-
t′ Hubbard model to clarify the effects of the adjacent CuO
2 layers on the stability of the superconductivity by using a many-variable variational Monte Carlo method. We calculate the superconducting correlation at long distance and zero temperature, and the amplitude of the superconducting gap functions estimated from the momentum distribution as the observables correlated with
Tcopt. It is found that the in-plane superconducting correlation is not enhanced in comparison with that in the single-layer
t-
t′ Hubbard model. The superconducting correlations of the bilayer Hamiltonian are significantly small in the overdoped region in comparison with those of single-layer Hamiltonian, which is attributed to the van Hove singularity. In addition, we found that the amplitude of the superconducting gap functions is also similar in both the single-layer and bilayer
t-
t′ Hubbard model at the optimal doping. Therefore, we conclude that the adjacent Hubbard layers are not relevant to the enhancement of
Tcopt in the bilayer cuprates. Possible origins of the enhanced
Tcopt other than the adjacent layers are also discussed.
A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon interlayer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping ${\ensuremath{\delta}}_{c}$ due to the formation of excitons. A spin-liquid-insulator (SLI) phase is thus realized without the lattice frustration. The critical value ${\ensuremath{\delta}}_{c}$ sensitively depends on the interlayer interaction strength. In the $t\text{\ensuremath{-}}J$ model description of each layer with the
d-wave pairing, ${\ensuremath{\delta}}_{c}$ marks the crossover between SLI and
d-wave superconductor. The SLI phase, despite being nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the $t\text{\ensuremath{-}}J$ model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.
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.