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.
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.
With the hierarchical Green’s function approach, we study a doped Mott insulator described with the Hubbard model by analytically solving the equations of motion of an one-particle Green’s function and related multiple-point correlation functions, and find that the separation of the spin and charge degrees of freedom of the electrons is an intrinsic character of the doped Mott insulator. For enough of large on-site repulsive Coulomb interaction, we show that the spectral weight of the one-particle Green’s function is proportional to the hole doping concentration that is mainly produced by the charge fluctuation of electrons, while the excitation spectrum of the electrons is composed of two parts: One is contributed by the spin fluctuation of the electrons, which is proportional to the hole doping concentration, and another one is coming from the coupling between the charge and spin fluctuations of the electrons that takes the maximum at undoping. All of these low energy/temperature physical properties originate from the strong on-site Coulomb interaction. The present results are consistent with the spectroscopy observations of the cuprate superconductors and the numerical calculations in normal state above the pseudogap regime.
We contrast the transport properties (dc resistivity, Seebeck coefficient), optical conductivity, spectral functions, dynamical magnetic susceptibility, and the nuclear magnetic resonance
1/T1 spin-lattice relaxation rate of the repulsive and attractive infinite-dimensional Hubbard models in the paramagnetic phase for a generic band filling. The calculations are performed in a wide temperature interval using the dynamical mean-field theory with the numerical renormalization group as the impurity solver. The attractive case exhibits significantly more complex temperature dependencies which can be explained by the behavior of the half-filled Hubbard model in external magnetic field with constant magnetization, to which the attractive Hubbard model maps through the partial particle-hole transformation. The resistivity is nonmonotonous for the strongly attractive case: it peaks significantly above the Mott-Ioffe-Regel value at a temperature
Tmax where the quasiparticle band disappears. For both signs of
U we find particle-hole asymmetry in the self-energy at low energies, but with the opposite kind of excitations having longer lifetime. This leads to a strong suppression of the slope of the Seebeck coefficient in the attractive case rather than an enhancement as in the repulsive case. The spin-lattice relaxation rate in the strongly attractive case has a nonmonotonic temperature dependence, thereby revealing the pairing fluctuations.
The Extremely Correlated Fermi Liquids (ECFL) theory is reviewed as a framework for understanding the
t-
J model in metallic systems close to the Mott insulating limit. This overview presents the underlying ideas and the resulting equations in a form accessible to nonexperts. We compare theoretical results with all available resistivity data for single-layer High-T
c systems, and with some spectral data. The highlighted results include a density dependent quasilinear T-dependence in resistivity, an unusually small quasiparticle weight, and distinct low-temperature emergent scales that dominate transport, thermodynamics and spectral properties of single-layer High T
c systems. Suggestions are made for further experiments to probe the physics of these challenging quantum many-body systems.
The theoretical investigation of spectral functions and pseudogap in systems with strongly correlated electrons is discussed, with the emphasis on the single-band t-J model as relevant for superconducting cuprates. The evidence for the pseudogap features from numerical studies of the model is presented. One of the promising methods to study spectral functions is the method of equations of motion. The latter can deal systematically with the local constraints and projected fermion operators inherent for strongly correlated electrons. In the evaluation of the self energy the decoupling of spin and single-particle fluctuations is performed. In an undoped antiferromagnet the method reproduces the selfconsistent Born approximation (SCBA). For finite doping the approximation evolves into a paramagnon contribution which retains large incoherent contribution in the hole part. On the other hand, the contribution of longer-range spin fluctuations is essential for the emergence of the pseudogap. The latter shows up at low doping in the effective truncation of the large Fermi surface, reduced electron density of states and at the same time reduced quasiparticle density of states at the Fermi level.