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

Rømer, Astrid T.; Maier, Thomas A.; Kreisel, Andreas; Eremin, Ilya; Hirschfeld, P. J.; Andersen, Brian M.

doi:10.1103/PhysRevResearch.2.013108

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

Journal Article · Fri Jan 31 00:00:00 EST 2020 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.2.013108· OSTI ID:1596391

;

; Eremin, Ilya; Hirschfeld, P. J.;

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_x²-y²-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 d_xy 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.

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Research Organization:: Univ. of Florida, Gainesville, FL (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; Lundbeckfond fellowship

Grant/Contract Number:: FG02-05ER46236; A9318; AC05-00OR22725

OSTI ID:: 1596391

Alternate ID(s):: OSTI ID: 1603796; OSTI ID: 1606663

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Vol. 2 Journal Issue: 1; ISSN 2643-1564

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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