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arXiv:2108.11428

Anomalous Resistivity at Weak Coupling

Thomas G. Kiely, Erich J. Mueller

Published Aug 25, 2021• 0 citations
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Abstract

Recent cold atom experiments have observed bad and strange metal behaviors in strongly-interacting Fermi-Hubbard systems. Motivated by these results, we calculate the thermoelectric transport properties of a 2D Fermi-Hubbard system in the weak coupling limit using quantum kinetic theory. We find that many features attributed to strong correlations are also found at weak coupling. In particular, for temperatures $T\gtrsim t$ the electrical resistivity is nearly linear in temperature despite the fact that the quasiparticle scattering rate is non-linear and changes by nearly an order of magnitude. We argue that this asymptotic behavior is a general feature of systems with a finite spectral width, which implies that there is no MIR bound on the resistivity in single-band models. Due to nesting, the $T$-linear resistivity persists down to $T=0$ at half filling. Our work sheds light on the transport regime in ultracold atom experiments, which can differ substantially from that of condensed matter systems. Disentangling these band-structure effects from the physics of strong correlations is a major challenge for future experiments.

DOI
10.48550/arxiv.2108.11428

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Recent cold atom experiments have observed bad and strange metal behaviors in strongly-interacting Fermi-Hubbard systems. Motivated by these results, we calculate the thermoelectric transport properties of a 2D Fermi-Hubbard system in the weak coupling limit using quantum kinetic theory. We find that many features attributed to strong correlations are also found at weak coupling. In particular, for temperatures T≳tT\gtrsim tT≳t the electrical resistivity is nearly linear in temperature despite the fact that the quasiparticle scattering rate is non-linear and changes by nearly an order of magnitude. We argue that this asymptotic behavior is a general feature of systems with a finite spectral width, which implies that there is no MIR bound on the resistivity in single-band models. Due to nesting, the TTT-linear resistivity persists down to T=0T=0T=0 at half filling. Our work sheds light on the transport regime in ultracold atom experiments, which can differ substantially from that of condensed matter systems. Disentangling these band-structure effects from the physics of strong correlations is a major challenge for future experiments.
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Quantum simulations are quickly becoming an indispensable tool for studying particle transport in correlated lattice models. One of the central topics in the study of transport is bad-metal behavior, characterized by the direct-current resistivity linear in temperature. In the fermionic Hubbard model, optical conductivity has been studied extensively, and a recent optical lattice experiment demonstrated bad-metal behavior in qualitative agreement with theory. Far less is known about transport in the bosonic Hubbard model. We investigate the conductivity in the Bose-Hubbard model and focus on the regime of strong interactions and high temperatures. We use numerically exact calculations for small lattice sizes. At weak tunneling, we find multiple peaks in the optical conductivity that stem from the Hubbard bands present in the many-body spectrum. This feature slowly washes out as the tunneling rate gets stronger. At high temperature, we identify a regime of TTT-linear resistivity, as expected. When the interactions are very strong, the leading inverse-temperature coefficient in conductivity is proportional to the tunneling amplitude. As the tunneling becomes stronger, this dependence takes quadratic form. At very strong coupling and half filling, we identify a separate linear resistivity regime at lower temperature, corresponding to the hard-core boson regime. Additionally, we unexpectedly observe that at half filling, in a big part of the phase diagram, conductivity is an increasing function of the coupling constant before it saturates at the hard-core-boson result. We explain this feature based on the analysis of the many-body energy spectrum and the contributions to conductivity of individual eigenstates of the system.
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|U|/t=6∣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 UUU. More strikingly, the similarity persists to temperatures well below ∣U∣|U|∣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.
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Strange or bad metallic transport, defined by incompatibility with the conventional quasiparticle picture, is a theme common to many strongly correlated materials, including high-temperature superconductors. The Hubbard model represents a minimal starting point for modeling strongly correlated systems. Here we demonstrate strange metallic transport in the doped two-dimensional Hubbard model using determinantal quantum Monte Carlo calculations. Over a wide range of doping, we observe resistivities exceeding the Mott-Ioffe-Regel limit with linear temperature dependence. The temperatures of our calculations extend to as low as 1/40 of the noninteracting bandwidth, placing our findings in the degenerate regime relevant to experimental observations of strange metallicity. Our results provide a foundation for connecting theories of strange metals to models of strongly correlated materials.