TY - JOUR

T1 - Pairing in the two-dimensional Hubbard model from weak to strong coupling

AU - Romer, Astrid T.

AU - Maier, Thomas A.

AU - Kreisel, Andreas

AU - Eremin, Ilya

AU - Hirschfeld, P. J.

AU - Andersen, Brian M.

PY - 2020/1/31

Y1 - 2020/1/31

N2 - 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 among these three methods, implying adiabatic continuity between weak- and strong-coupling pairing solutions of the Hubbard model. The d(x)(2)-(2)(y) - 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, a 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.

AB - 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 among these three methods, implying adiabatic continuity between weak- and strong-coupling pairing solutions of the Hubbard model. The d(x)(2)-(2)(y) - 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, a 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.

KW - WAVE SUPERCONDUCTIVITY

KW - SPIN-FLUCTUATION

KW - INSTABILITIES

KW - MECHANISM

U2 - 10.1103/PhysRevResearch.2.013108

DO - 10.1103/PhysRevResearch.2.013108

M3 - Journal article

VL - 2

JO - Physical Review Research

JF - Physical Review Research

SN - 2643-1564

IS - 1

M1 - 013108

ER -