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In previous studies of the half-filled bilayer attractive Hubbard model Prasad et al. , Phys. Rev. A 89, 043605 (2014) ; Prasad, Phys. Rev. B 106, 184506 (2022), it has been shown that the clean system has a band-insulator (BI) to superfluid (SF) quantum phase transition. In this paper, we append the effects of random on-site disorder on the kinetic energy, double occupancy, and the pair-pair correlations in the bilayer model. Using the determinant quantum Monte Carlo simulation, we observe that the on-site random disorder plays a significant role in the localization of on-site pairs, and hence in the reduction of the effective hopping. This results in an increase of the double occupancy, which is an effect that is similar to the attractive interaction. We find no change in the critical value of the interaction at which the model undergoes a transition from the BI to SF regime, even though the pair-pair correlations get suppressed for finite on-site disorder strengths V₃/t=0. 1--0. 8. We also confirm that the weak-disorder suppresses the SF phase largely in the strong-coupling limit. Hence the region of the SF phase reduces in the presence of random on-site disorder. Finally, through finite-size scaling, we have estimated the critical disorder strength V₃^c/t1. 44 at |U|/t=5.
Prasad et al. (Wed,) studied this question.