We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension
d as well as the infinite-
d limit, arbitrary electron density
n, and both finite and infinite repulsion
U. We use moment-reconstruction methods to obtain the one-electron spectral function, the self-energy, and the optical conductivity. They are all smooth functions at high temperature and, at large
U, they are featureless with characteristic widths of the order of the lattice hopping parameter
t. In the infinite-
d limit, we compare the series expansion results with accurate numerical renormalization group and interaction expansion quantum Monte Carlo results. We find excellent agreement down to surprisingly low temperatures, throughout most of the bad-metal regime, which applies for $T\ensuremath{\gtrsim}(1\ensuremath{-}n)D$, the Brinkman-Rice scale. The resistivity increases linearly in
T at high temperature without saturation. This results from the
1/T behavior of the compressibility or kinetic energy, which play the role of the effective carrier number. In contrast, the scattering time (or diffusion constant) saturates at high
T. We find that $\ensuremath{\sigma}(n,T)\ensuremath{\approx}(1\ensuremath{-}n)\ensuremath{\sigma}(n=0,T)$ to a very good approximation for all
n, with $\ensuremath{\sigma}(n=0,T)\ensuremath{\propto}t/T$ at high temperatures. The saturation at small
n occurs due to a compensation between the density dependence of the effective number of carriers and that of the scattering time. The
T dependence of the resistivity displays a kneelike feature which signals a crossover to the intermediate-temperature regime where the diffusion constant (or scattering time) starts increasing with decreasing
T. At high temperatures, the thermopower obeys the Heikes formula, while the Wiedemann-Franz law is violated with the Lorenz number vanishing as
1/T2. The relevance of our calculations to experiments probing high-temperature transport in materials with strong electronic correlations or ultracold atomic gases in an optical lattice is briefly discussed.
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≳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.
High-temperature bad-metal transport has been recently studied both theoretically and in experiments as one of the key signatures of strong electronic correlations. Here we use the dynamical mean field theory and its cluster extensions, as well as the finite-temperature Lanczos method to explore the influence of lattice frustration on the thermodynamic and transport properties of the Hubbard model at high temperatures. We consider the triangular and the square lattices at half-filling and at 15% hole doping. We find that for $T\ensuremath{\gtrsim}1.5t$ the self-energy becomes practically local, while the finite-size effects become small at lattice size $4\ifmmode\times\else\texttimes\fi{}4$ for both lattice types and doping levels. The vertex corrections to optical conductivity, which are significant on the square lattice even at high temperatures, contribute less on the triangular lattice. We find approximately linear temperature dependence of dc resistivity in doped Mott insulator for both types of lattices.
Results for the optical conductivity and resistivity of the Hubbard model in infinite spatial dimensions are presented. At half-filling we observe a gradual crossover from a metal with a Drude peak at ω = 0 in the optical conductivity to an insulator as a function of U for temperatures above the antiferromagnetic phase transition. When doped, the "insulator" becomes a Fermi liquid with a corresponding temperature dependence of the optical conductivity and resistivity. We find a T 2 -coefficient in the low-temperature resistivity which suggests that the carriers in the system acquire a considerable mass-enhancement due to the strong local correlations. At high temperatures, a crossover into a semi-metallic regime takes place.
Two-dimensional hard core bosons suffer strong scattering in the high-temperature resistive state at half filling. The dynamical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ is calculated using nonperturbative tools such as continued fractions, series expansions, and exact diagonalization. We find a large temperature range with linearly increasing resistivity and broad dynamical conductivity, signaling a breakdown of Boltzmann-Drude quasiparticle transport theory. At zero temperature, a high-frequency peak in $\ensuremath{\sigma}(\ensuremath{\omega})$ appears above a ``Higgs mass'' gap and corresponds to order-parameter magnitude fluctuations. We discuss the apparent similarity between conductivity of hard core bosons and phenomenological characteristics of cuprates, including the universal scaling of Homes et al. [Nature (London) 430, 539 (2004)].
Non-saturating high-temperature resistivity ("bad metal"), T-linear low-temperature resistivity ("strange metal"), and a crossover to activation-free growth of the resistivity in the low-temperature limit ("weak insulator") are among the most exotic behaviors widely observed in many strongly correlated materials for decades that defy the standard Fermi liquid description of solids. Here we investigate these puzzling behaviors by computing temperature-dependent optical conductivity of an emergent Bose liquid and find that it reproduces all the unexplained features of the experiments, including a featureless continuum and a well-known mid-infrared peak. Amazingly and with physically intuitive mechanisms, the corresponding doping- and temperature-dependent resistivity displays the bad metal and strange metal simultaneously and sometimes weak insulating behaviors as well. The unification of all these non-Fermi liquid behaviors in a single model suggests that a new quantum state of matter, namely the emergent Bose liquid, will guide the development of the next generation of solid state physics.