Toschi, Alessandro | Search NASA

DOE OSTI2022

Mechanism of superconductivity in the Hubbard model at intermediate interaction strength

We study the fluctuations responsible for pairing in the d -wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d -wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Dynamical vertex approximation for many-electron systems with spontaneously broken SU(2) symmetry

We generalize the formalism of the dynamical vertex approximation (DΓA)—a diagrammatic extension of the dynamical mean-field theory (DMFT)—to treat magnetically ordered phases. To this aim, we start by concisely illustrating the many-electron formalism for performing ladder resummations of Feynman diagrams in systems with broken SU(2) symmetry associated to ferromagnetic (FM) or antiferromagnetic (AF) order. We then analyze the algorithmic simplifications introduced by taking the local approximation of the two-particle irreducible vertex functions in the Bethe-Salpeter equations, which defines the ladder implementation of DΓA for magnetic systems. The relation of this assumption with the DMFT limit of large coordination-number/high dimensions is explicitly discussed. As a last step, we derive the expression for the ladder DΓA self-energy in the FM- and AF-ordered phases of the Hubbard model. The physics emerging in the AF-ordered case is explicitly illustrated by means of approximated calculations based on a static mean-field input for DΓA equations. The results obtained capture fundamental aspects of both metallic and insulating ground states of two-dimensional antiferromagnets, providing a reliable compass for future, more extensive applications of our approach. Furthermore, possible routes to further develop diagrammatic-based treatments of magnetic phases in correlated electron systems are briefly outlined in the Conclusions.

2-dimensional systems↗