Many strongly correlated systems exhibit strange metallic behavior in certain parameter regimes characterized by anomalous transport properties that are irreconcilable with a Fermi-liquid-like description in terms of quasiparticles. The Hubbard model is a standard theoretical starting point to examine the properties of such systems and also exhibits non-Fermi-liquid behavior in simulations. Here we analytically study the two-dimensional hole-doped Hubbard model in the large
U limit, first identifying a doping-induced percolation transition in the low-energy sector occurring at a definite critical doping
pc depending on lattice structure. Using the critical properties near this transition we rewrite the Hubbard Hamiltonian and motivate a low-energy lattice-independent large-
N model with distinct non-Fermi-liquid properties. We show that this model has linear-in-
T resistivity with doping-dependent slope maximized at
p=pc and power-law optical conductivity ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$. Though the parameters used in developing this theory mean it cannot be directly applied to the cuprate superconductors, we nevertheless reproduce several important phenomena observed in their strange metal phase and also predict these same qualitative behaviors to manifest in other lattices near concrete hole dopings.
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.
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.
A refined semi-holographic non-Fermi liquid model, in which carrier electrons hybridize with operators of a holographic critical sector, has been proposed recently for strange metallic behavior. The model, consistently with effective theory approach, has two couplings whose ratio is related to the doping. We explain the origin of the linear-in-T resistivity and strange metallic behavior as a consequence of the emergence of a universal form of the spectral function which is independent of the model parameters when the ratio of the two couplings take optimal values determined only by the critical exponent. This universal form fits well with photoemission data of copper oxide samples for under/optimal/over-doping with a fixed exponent over a wide range of temperatures. We further obtain a refined Planckian dissipation scenario in which the scattering time
τ=f⋅ℏ/(kBT), with
f being
O(1) at strong coupling, but
O(10) at weak coupling.
"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.
To clarify the origin of the pseudogap and strange metal states as well as their mutual relationship in cuprate superconductors, a comprehensive study on the spectral function, Fermi surface, resistivity and dynamical spin susceptivity of the Hubbard model on the square lattice has been conducted by means of the ladder dual-fermion approximation with an electron self-energy correction. It is found that the appearance of these two states requires that the characteristic hole concentration below which the Mott-Heisenberg and Slater mechanisms of electron localization occurs
pMS nearly coincides with the hole concentration where the Van Hove singularity (VHS) point is placed at the vicinity of the Fermi level. When this condition is met the VHS point is pinned at which the nesting condition of the antiferromagnetic (AFM) fluctuation is fulfilled almost everywhere on the Fermi surface in wide range of the hole concentration in a metallic state, i.e., the strange metal state. The spin fluctuation of the strange metal state is nearly quantum critical and the dynamical spin susceptivity is well described by overdamped spin wave having the
ω/T scaling with the relaxation rate at the Planckian limit. Because of these distinctive features of the strange metal state, the
k dependence of scattering rate of electrons is small and electrons behave as the marginal Fermi liquid, resulting in
T-linear resistivity. In contrast, the pseudogap state is magnetically in the renormalized classical regime and the pseudogap is formed near the X point where the nesting condition of the short-range AFM order is fulfilled.