Spin scattering turns complex at strong coupling: the key to pseudogap and Fermi arcs in the Hubbard model

Abstract

We analyze the pseudogap phenomenon of hole-doped cuprates via a Feynman-diagrammatic inspection of the Hubbard model. Our approach captures the pivotal interplay between Mott localization and Fermi surface topology beyond weak-coupling spin fluctuations, which open a spectral gap near hot spots. We show that strong coupling and particle-hole asymmetry give rise to another mechanism: the spin-fermion vertex develops a large imaginary part. While its real part always suppresses the electronic lifetime, the imaginary part has a twofold effect. For antinodal fermions a gap opening is boosted; conversely, around the node Fermi arcs are protected.

Mechanism of Superconductivity in the Hubbard Model at Intermediate Interaction Strength

“…The microscopic picture of superconductivity emerging from our analysis agrees well with recent studies of the description of the non-superconducting pseudogap regime: While spin-fluctuations were identified as the predominant mechanism of the pseudogap [14,31,32], differences with respect to the predictions of conventional spin-fluctuation theory were found and traced [43] to the imaginary part of the dynamical scattering amplitude between electrons and spin fluctuations, which is absent in conventional approaches [43].…”

The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model

“…5). On the other hand, we found in recent investigations that, as soon as fermionic states are destroyed due to the feedback from the spin fluctuations, this requirement is lifted and γ sp rises again for those k where a pseudogap opens, resulting in a nodal/antinodal dichotomy of γ sp with respect to k [3,38]. There hence exists a subtle interplay between bosonic fluctuations, Fermi surface features, and the Yukawa couplings, which needs to be considered when dependencies of the latter are neglected or parametrized.…”

“…The remaining U -irreducible diagrams, to which we refer as multi-boson exchange (M ), do not permit a representation in terms of γ, W alone, but instead capture repeated exchange of bosons. The resulting picture of bosons mediating effective interactions [17] is physically appealing and remains valid even at strong coupling [3,18]. Further, it is plausible that fewer Feynman diagrams correspond to reduced computational cost in practical applications.…”

“…It is hard to go beyond the GW approximation, although it is desirable in cases of gross quantitative discrepancies to experiment [2] or, for example, at strong coupling where vertex corrections may alter the interaction between fermions and bosons qualitatively [3]. However, it is not a trivial task to even define proper strategies to extend the GW approximation: as usual, derivability from a potential leads to approximations that respect conservation laws [4]; on the other hand one may also prefer, for example, a positive semi-definite real-axis spectrum as a stringent criterion [5,6]; or aim at including strong correlation effects [7,8].…”

Magnetic properties and pseudogap formation in infinite-layer nickelates: insights from the single-band Hubbard model

“…The exact location of the change from a weak-coupling to a strong-coupling pseudogap regime is a matter of current debate. Three indicators for this change can be mentioned: (i) a sudden increase in electronic correlations leading to a change in Fermi surface topology [60], (ii) this strong correlation regime hosts relatively shortranged correlations with the occurrence of (partial) localization [40,63] and (iii) the electron-boson coupling vertex develops a significant imaginary part [75,76]. Our investigations of (i) and (ii) in this manuscript by means of the DΓA, hence, allow us to characterize the found pseudogap as driven by strong coupling (Mott) physics.…”