Robust Strange Metallicity across Attractive and Repulsive Hubbard Models

Abstract

Using determinant quantum Monte Carlo simulations, we compare charge transport in the two-dimensional attractive and repulsive Hubbard models at strong coupling, $|U|/t=6$. Although the interaction with opposite signs generates qualitatively different low-energy spin, charge, and pairing correlations, both exhibit approximately linear-in-temperature resistivity over a broad intermediate- and high-temperature regime. At asymptotically high temperature this common behavior follows from the moment expansion of the conductivity, whose leading contribution is even in $U$. More strikingly, the similarity persists to temperatures well below $|U|$, where strong interaction-dependent correlations have already developed, and also irrespective of whether resistivity crosses the MIR limit. Using the Nernst--Einstein relation, we find that the common linear-in-temperature resistivity is primarily associated with an approximately Curie-like charge compressibility and weakly temperature-dependent diffusivity. The two models separate only at lower temperatures, where the attractive model develops a pronounced feature in the charge diffusivity correlated with signatures of pair formation. These results show that linear-in-temperature incoherent transport in the Hubbard model can be remarkably insensitive to the microscopic nature of the low-energy correlations. Our results suggest that transport in the incoherent regime appears insensitive to what the system will ultimately become at low temperature; the distinction between competing low-energy states becomes visible only when their characteristic correlations acquire sufficiently long spatial or temporal coherence.