Properties of the two-dimensional Hubbard model with nearest-neighbor hopping are under scrutiny in cold-atom experiments and diagrammatic quantum Monte Carlo. Given the controlled nature of these approaches, it is timely to make predictions about strange-metal behavior and its relation to quantum-critical properties. Even for interaction strengths below the Mott transition, several peculiarities occur at the quantum critical point separating Fermi liquid and incommensurate spin-density wave order. Here, we predict, using the non-perturbative improved two-particle self-consistent approach, that for correlation lengths ranging from about one to one hundred lattice spacings, Kohn anomalies on the underlying Fermi surface lead to unconventional critical exponents. The temperature dependence of the single-particle self-energy acquires strong momentum dependence along the Fermi surface with no clear evidence of Landau quasiparticles. Nevertheless, we observe strange-metal behavior, namely, resistivity that scales linearly with temperature as
T→0. Our work shows that a linear temperature dependence of resistivity arises without a linear-in-temperature self-energy along the Fermi surface, as is often assumed.
We investigate the effects of static, diagonal disorder in the
d=∞ Hubbard model by treating the dynamical effects of local Hubbard correlations and disorder on an equal footing. This is achieved by a proper combination of the iterated perturbation theory and the coherent potential approximation. Within the paramagnetic phase, we find that the renormalized Fermi liquid metal phase of the pure Hubbard model is stable against disorder for small disorder strengths. With increasing disorder, strong resonant scattering effects destroy low-energy Fermi liquid coherence, leading to an {\it incoherent} metallic non-FL state off half-filling. Finally, for large enough disorder, a {\it continuous} transition to the Mott-Anderson insulating phase occurs. The nature of the non-FL metallic phase, as well as the effects of the low energy coherence (incoherence) on optical conductivity and electronic Raman spectra, are considered in detail.
Finding microscopic models for metallic states that exhibit quantum critical properties is a major theoretical challenge. We calculate the dynamical local spin susceptibility $\ensuremath{\chi}(T,\ensuremath{\omega})$ for a Hubbard model at half-filling using dynamical mean-field theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite-temperature critical point. The signature of the latter is $\ensuremath{\omega}/T$ scaling, where $\ensuremath{\omega}$ is the frequency and
T is the temperature. Our results are consistent with previous results showing scaling of the dc electrical conductivity, and they are relevant to experiments on organic charge-transfer salts.
Abstract We investigate the finite temperature properties of the half filled Hubbard model in two dimensions, with onsite interaction ( U ), in presence of (frustrating) next nearest neighbor hopping ( t ′) using a semiclassical approximation scheme. We show that introduction of t ′ results in a finite temperature pseudogapped (PG) phase that separates the small U Fermi liquid and large U Mott insulator. We map out the PG to normal metal crossover temperature scale ( T *) as a function of U and t ′. We demonstrate that in the PG phase, the quadratic dependence of resistivity on temperature is violated due to thermally induced spin fluctuations. We conclude with exact diagonalization calculations, that complement our finite temperature results, and indicate the presence of a frustration driven PG state between the Fermi liquid and the Mott insulator at zero temperature as well.
We have studied the one-dimensional periodic, symmetric Anderson model at half filling in the presence of disorder using finite-temperature quantum Monte Carlo techniques. We have examined for the first time the disorder both in hybridization between the local f-orbitals and the conduction electrons and in the local f-site energy, using a uniform distribution of width . The f-orbital local magnetic moment, the uniform magnetic susceptibility, the charge compressibility, and the nearest-neighbour magnetic correlation function have been calculated as a function of the disorder distribution width . We find that the disorder in hybridization has a dramatic effect on the low-temperature magnetic properties exhibiting a non-Fermi-liquid behaviour, and that for the range of temperature studied the magnetic susceptibility can be scaled by a power law with an exponent that is in agreement with recent experiments. On the other hand, disorder in the local f-orbital energy level does not show a nonFermi liquid behaviour.
Recent progress in extremely correlated Fermi liquid theory (ECFL) and the dynamical mean field theory (DMFT) enables us to accurately compute in the $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit the resistivity of the $t\ensuremath{-}J$ model after setting $J\ensuremath{\rightarrow}0$. This is also the $U=\ensuremath{\infty}$ Hubbard model. Since
J is set to zero, our study isolates the dynamical effects of the single occupation constraint enforced by the projection operator originally introduced by Gutzwiller. We study three densities
n=.75,.8,.85 that correspond to a range between the overdoped and optimally doped Mott insulating state. We delineate four distinct regimes separated by three crossovers, which are characterized by different behaviors of the resistivity $\ensuremath{\rho}$. We find at the lowest temperature
T a Gutzwiller correlated Fermi liquid regime with $\ensuremath{\rho}\ensuremath{\propto}{T}^{2}$ extending up to an effective Fermi temperature that is dramatically suppressed from the noninteracting value by the proximity to half filling, $n\ensuremath{\sim}1$. This is followed by a Gutzwiller correlated strange metal regime with $\ensuremath{\rho}\ensuremath{\propto}(T\ensuremath{-}{T}_{0})$, i.e., a linear resistivity extrapolating back to $\ensuremath{\rho}=0$ at a positive
T0. At a higher temperature scale this crosses over into the bad metal regime with $\ensuremath{\rho}\ensuremath{\propto}(T+{T}_{1})$, i.e., a linear resistivity extrapolating back to a finite resistivity at
T=0 and passing through the Ioffe-Regel-Mott value where the mean free path is a few lattice constants. This regime finally gives way to the high
T metal regime, where we find $\ensuremath{\rho}\ensuremath{\propto}T$, i.e., a linear resistivity extrapolating back to zero at
T=0. The present work emphasizes the first two, i.e., the two lowest temperature regimes, where the availability of an analytical ECFL theory is of help in identifying the changes in related variables entering the resistivity formula that accompanies the onset of linear resistivity, and the numerically exact DMFT helps to validate the results. We also examine thermodynamical variables such as the magnetic susceptibility, compressibility, heat capacity, and entropy and correlate changes in these with the change in resistivity. This exercise casts valuable light on the nature of charge and spin correlations in the Gutzwiller correlated strange metal regime, which has features in common with the physically relevant strange metal phase seen in strongly correlated matter.