Strongly correlated metals often display anomalous transport, including T-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for bad metals, by restoring in the well-known Hubbard model-with hopping t and on-site repulsion U-a "screened Coulomb" interaction between charge densities that decays exponentially with spatial separation. This interaction lifts the extensive degeneracy in the spectrum of the t=0 Hubbard model, allowing us to fully characterize the small t electric, thermal, and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe T-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Wiedemann-Franz law and a large thermopower that can undergo sign change.
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.
Bad metals exhibit approximately
T-linear dc resistivity beyond the Ioffe--Regel limit. That this behavior occurs in systems with radically different ground states suggests it is a generic manifestation of strong local correlations. We test this hypothesis in the infinite-
U Hubbard model with small hole densities using exact diagonalization to compute thermodynamic and transport properties of finite clusters. Upon cooling, we find an intermediate temperature range, an electronic analogue of the ``semi-quantum regime'' of liquid helium, in which quantum effects produce a roughly
T-independent compressibility, yet the resistivity is
T-linear and exceeds the Ioffe--Regel limit. Entry into this regime is accompanied by the formation of quasi-local ferromagnetic ``spin cages'' around doped holes, regions that facilitate local quantum motion embedded in a fluctuating spin background, analogous to the transient crystalline cages thought to control incoherent transport in semi-quantum liquid helium. Remarkably, despite the simplicity of the model, the bad metal behavior found here resembles that seen in various material platforms.
Electrical current in conventional metals is carried by electrons that retain their individual character. Bad metals, such as the normal state of some high-temperature superconductors, violate this scenario, and the complete picture for their behavior remains unresolved. Here, we report phenomena consistent with bad-metal behaviour in an optical-lattice Hubbard model by measuring the transport lifetime for a mass current excited by stimulated Raman transitions. We demonstrate incompatibility with weak-scattering theory and key characteristics of bad metals: anomalous resistivity scaling consistent with T-linear behavior, the onset of incoherent transport, and the approach to the Mott-Ioffe-Regel limit. Our work demonstrates a direct method for determining the transport lifetime, which is critical to theory but difficult to measure in materials, and exposes minimal ingredients for bad-metal behavior.
We report the discovery of phenomena consistent with bad-metal relaxation dynamics in the metallic regime of an optical-lattice Hubbard model. The transport lifetime induced by inter-particle scattering for a mass current of atoms excited by stimulated Raman transitions is measured, and the corresponding analog of resistivity is inferred. By exploring a range of temperature, we demonstrate incompatibility with weak-scattering theory and a key characteristic of bad metals: anomalous resistivity scaling consistent with
T-linear behavior. We also observe the onset of two behaviors---incoherent transport and the approach to the Mott-Ioffe-Regel limit---associated with bad metals. The interaction and temperature scaling of resistivity are verified to be consistent with dynamic mean-field theory (DMFT) predictions of a bad metal, which is associated with the reduction of quasiparticle weight by strong interactions.
Good metals are characterized by diffusive transport of coherent quasiparticle states and the resistivity is much less than the Mott-Ioffe-Regel (MIR) limit,
e2ha, where
a is the lattice constant. In bad metals, such as many strongly correlated electron materials, the resistivity exceeds the Mott-Ioffe-Regel limit and the transport is incoherent in nature. Hartnoll, loosely motivated by holographic duality (AdS/CFT correspondence) in string theory, recently proposed a lower bound to the charge-diffusion constant, $D\ensuremath{\gtrsim}\ensuremath{\hbar}{v}_{F}^{2}/({k}_{B}T)$, in the incoherent regime of transport, where
vF is the Fermi velocity and
T the temperature. Using dynamical mean-field theory (DMFT) we calculate the charge-diffusion constant in a single band Hubbard model at half filling. We show that in the strongly correlated regime the Hartnoll's bound is violated in the crossover region between the coherent Fermi-liquid region and the incoherent (bad metal) local moment region. The violation occurs even when the bare Fermi velocity
vF is replaced by its low-temperature renormalized value
vF∗. The bound is satisfied at all temperatures in the weakly and moderately correlated systems as well as in strongly correlated systems in the high-temperature region where the resistivity is close to linear in temperature. Our calculated charge-diffusion constant, in the incoherent regime of transport, also strongly violates a proposed quantum limit of spin diffusion, ${D}_{s}\ensuremath{\sim}1.3\ensuremath{\hbar}/m$, where
m is the fermion mass, experimentally observed and theoretically calculated in a cold degenerate Fermi gas in the unitary limit of scattering.
Many metallic quantum materials display anomalous transport phenomena that defy a Fermi liquid description. Here, we use numerical methods to calculate thermal and charge transport in the doped Hubbard model and observe a crossover separating high- and low-temperature behaviors. Distinct from the behavior at high temperatures, the Lorenz number [Formula: see text] becomes weakly doping dependent and less sensitive to parameters at low temperatures. At the lowest numerically accessible temperatures, [Formula: see text] roughly approaches the Wiedemann-Franz constant [Formula: see text], even in a doped Mott insulator that lacks well-defined quasiparticles. Decomposing the energy current operator indicates a compensation between kinetic and potential contributions, which may help to clarify the interpretation of transport experiments beyond Boltzmann theory in strongly correlated metals.