本文采用约束路径量子蒙特卡罗方法系统地探讨了双层哈伯德模型中的激子态特性。计算结果表明，当空穴和电子掺杂浓度低于0.08时，由层间单粒子隧穿强度表征的局域激子态被层间库仑相互作用V增强，且随着掺杂浓度的减小增强效应逐渐变强，而当空穴和电子掺杂浓度高于0.08时，局域激子态却被V减弱。该结果与已发表的有限温度结果存在重要的差异。进一步的分析发现在整个掺杂区间，激子的长程空间关联函数随着V的增加而减小，表明研究的双层哈伯德模型中不存在激子序参量的长程序，即激子凝聚态。此外，层间库仑相互作用V对格点磁矩的影响很小。 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 temperatures. 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.
We formulated an effective theory for a single interlayer exciton in a bilayer quantum antiferromagnet, in the limit when the holon and doublon are strongly bound onto one interlayer rung by the Coulomb force. Upon using a rung linear spin-wave approximation of the bilayer Heisenberg model, we calculated the spectral function of the exciton for a wide range of the interlayer Heisenberg coupling α = J ⊥ / Jz . In the disordered phase at large α , a coherent quasi-particle peak appears, representing free motion of the exciton in a spin singlet background. In the Néel phase, which applies to more realistic model parameters, a ladder spectrum arises due to Ising confinement of the exciton. The exciton spectrum is visible in measurements of the dielectric function, such as c -axis optical conductivity measurements.
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⊥, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Liftshiz 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± pairing correlations in the large
t⊥ 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.