Pairing in the two-dimensional Hubbard model from weak to strong coupling

Abstract

The Hubbard model is the simplest model that is believed to exhibit superconductivity arising from purely repulsive interactions, and has been extensively applied to explore a variety of unconventional superconducting systems. Here we study the evolution of the leading superconducting instabilities of the single-orbital Hubbard model on a two-dimensional square lattice as a function of onsite Coulomb repulsion U and band filling by calculating the irreducible particle-particle scattering vertex obtained from dynamical cluster approximation (DCA) calculations, and compare the results to both perturbative Kohn-Luttinger (KL) theory as well as the widely used random phase approximation (RPA) spin-fluctuation pairing scheme. Near half-filling we find remarkable agreement of the hierarchy of the leading pairing states between these three methods, implying adiabatic continuity between weak-and strong-coupling pairing solutions of the Hubbard model. The d x 2 −y 2 -wave instability is robust to increasing U near half-filling as expected. Away from half filling, the predictions of KL and RPA at small U for transitions to other pair states agree with DCA at intermediate U as well as recent diagrammatic Monte Carlo calculations. RPA results fail only in the very dilute limit, where it yields a dxy ground state instead of a p-wave state established by diagrammatic Monte Carlo and low-order perturbative methods, as well as our DCA calculations. We discuss the origins of this discrepancy, highlighting the crucial role of the vertex corrections neglected in the RPA approach. Overall, comparison of the various methods over the entire phase diagram strongly suggests a smooth crossover of the superconducting interaction generated by local Hubbard interactions between weak and strong coupling.I.

Ultrafast renormalization of the onsite Coulomb repulsion in a cuprate superconductor

“…Since the CT gap magnitude anticorrelates with the equilibrium superconducting T c in both theory and experiments [91,92], such reduction might be favorable to the onset of out-of-equilbrium pairing. Moreover, in a spin-fluctuation-mediated picture, the CT gap closure will be accompanied by a renormalization of the pairing interaction and of the spin fluctuation spectrum [33,93]. A lower CT gap will also increase the exchange interaction and, hence, the characteristic spin fluctuation energy [94].…”

Coupled Hubbard ladders at weak coupling: Pairing and spin excitations

“…Recent studies have shown that RPA-based weak coupling approaches describe certain behavior in Hubbard models remarkably well. For example, systematic studies of the leading pairing instabilities in a 2D square lattice Hubbard model with increasing Coulomb repulsion U found that weak coupling RPA predictions agreed exceptionally well [23] with those of non-perturbative quantum Monte Carlo dynamic cluster approximation (DCA) [24] results. Similarly, for a Hubbard model in a two-leg ladder geometry, RPA calculations within a fluctuation exchange approximation (FLEX) were shown to capture the main features of density matrix renormalization group (DMRG) results for the magnetic and charge dynamical response [25].…”

Origin of the maximal critical temperature disparities in one-layer cuprate superconductors

“…Numerical solution of the gap equation shows that the gap function decreases slowly like 1/ω at large ω and is often used at intermediate coupling 28 and at relevant relatively small frequencies can be approximated by its n = 0 component:…”