Contractor-renormalization study of Hubbard plaquette clusters

Abstract

We implement the contractor-renormalization method to study the checkerboard Hubbard model on various finite-size clusters as function of the inter-plaquette hopping t ′ and the on-site repulsion U at low hole doping. We find that the pair-binding energy and the spin gap exhibit a pronounced maximum at intermediate values of t ′ and U , thus indicating that moderate inhomogeneity of the type considered here substantially enhances the formation of hole pairs. The rise of the pairbinding energy for t ′ < t ′ max is kinetic-energy driven and reflects the strong resonating valence bond correlations in the ground state that facilitate the motion of bound pairs as compared to single holes. Conversely, as t ′ is increased beyond t ′ max antiferromagnetic magnons proliferate and reduce the potential energy of unpaired holes and with it the pairing strength. For the periodic clusters that we study the estimated phase ordering temperature at t ′ = t ′ max is a factor of 2-6 smaller than the pairing temperature.

Enhanced pairing in the checkerboard Hubbard ladder

“…The present study, along with a variety of other recent studies 5,8,9,22 , provide strong support for a number of intuitively appealing ideas concerning the physics of the superconducting T c in unconventional superconductors in which the pairing arises directly from the repulsive interactions between electrons: 1) The highest superconducting transition temperatures occur at intermediate interaction strength, when U is comparable to the band-width. (A corollary of this is that materials which are studied because of their high transition temperatures are also likely to exhibit more general signatures of lying in an intermediate coupling regime; here, theoretical results from both weak and strong coupling approaches must be extrapolated, at best, to the limits of their regimes of applicability.)…”

“…As we were completing this work, a contractor renormalization (CORE) study of the checkerboard Hubbard model in a 2D geometry was presented in Ref. 9, extending earlier CORE results for the uniform 2D Hubbard model 10 . Finite size effects were found to be large for t ′ > ∼ 0.8t, but in the smaller t ′ regime, where these effects are relatively small, the results of this new study are completely consistent with those of the earlier exact diagonalization studies 5 , and lead to conclusions concerning the optimal conditions for superconductivity that are similar to those obtained in the present ladder study.…”

Optimal inhomogeneity for pairing in Hubbard systems with next-nearest-neighbor hopping

“…Exact diagonalization of the 4 × 4 site system [10] has found a substantial maximum of the pair-binding energy at t ′ /t ≈ 0.5, U/t ≈ 8 and low hole doping. A similar pairing maximum, occurring at intermediate inhomogeneity levels t ′ /t ≈ 0.5−0.7 and interaction strengths U/t ≈ 5 − 8, was subsequently found in larger plaquette systems using the contractor renormalization (CORE) [11] and DMRG [12] methods. Furthermore, by calculating the other necessary ingredient for superconductivity, namely phase stiffness, these studies have provided evidence that optimal inhomogeneity likely exists also for the superconducting transition temperature, T c , and not just for the pairing scale.…”

Geometry dependence of the sign problem in quantum Monte Carlo simulations

“…Other examples are the 'plaquette' model studied by Scalapino 52 , Kivelson, 53 and others, [54][55][56][57]66 as a description of superconductivity arising from pair binding on 2 × 2 plaquettes, and the 1/5-depleted square lattice 23,58,59 for which the results in the left panel of Fig. 12 show the improvement of the sign by increasing the inter-plaquette hopping t ′ from zero.…”