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.
Correlated Electrons
In many materials, charge carriers are well described as noninteracting quasiparticles. However, in materials with strong correlations, this approximation can break down, leading to anomalous transport properties at high temperatures. Huang et al. used quantum Monte Carlo calculations to look for this so-called strange metal phase in the simplest two-dimensional model of interacting electrons, the Hubbard model. They found that the calculated resistivity had a linear temperature dependence when hole doping was introduced, as expected in the strange metal phase. This observation provides confidence that simplified models can be used to describe and understand the behavior of real materials, such as cuprate high-temperature superconductors.
Science , this issue p. [987][1]
[1]: /lookup/doi/10.1126/science.aau7063
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.
Abstract: The metal–insulator transition (MIT) constitutes one of the most profound and persistent problems in condensed matter physics, sitting at the intersection of electronic structure theory, many-body physics, and emergent quantum phenomena. Conventional band theory, which successfully classifies materials as metals or insulators according to the filling of their electronic bands, fails dramatically when confronted with a class of compounds transition metal oxides chief among them that ought to be metallic by band-counting arguments yet are robustly insulating in the laboratory. The resolution of this paradox required abandoning the independent-electron picture entirely and recognizing that strong Coulomb repulsion between electrons can, by itself, drive localization. This insight, formalized by Mott and later distilled into the Hubbard model, established correlation-driven insulation as a phenomenon distinct from band insulation. The present paper offers a theoretical exploration of the MIT problem, tracing its conceptual development from the Mott criterion through the Hubbard Hamiltonian, the Brinkman–Rice scenario of quasiparticle mass divergence, and the watershed development of dynamical mean-field theory (DMFT), which rendered the Mott transition quantitatively tractable for the first time. We argue that the competition between the electronic bandwidth and the on-site interaction encoded in the ratio U/W provides the unifying organizing principle for the field. Building toward the modern frontier, we examine how the Mott transition connects to quantum phase transitions and quantum criticality, where zero-temperature instabilities governed by quantum rather than thermal fluctuations produce non-Fermi-liquid behavior and anomalous scaling. Case studies of vanadium oxides, rare-earth nickelates, and doped cuprates illustrate the diversity and subtlety of real correlated materials. We conclude that the MIT remains a central and unresolved problem whose continued study is increasingly entangled with the development of quantum materials and quantum technologies. Keywords: Metal–Insulator Transition; Mott Insulator; Strongly Correlated Electrons; Hubbard Model; DMFT; Quantum Criticality; Quantum Materials; Condensed Matter Physics
Luttinger's theorem has long been taken as the key feature of Landau's Fermi liquid, which signals the presence of quasiparticles. Here, by the unbiased Monte Carlo method, violation of Luttinger's theorem is clearly revealed in the Falicov-Kimball (FK) model, indicating a robust correlation-driven non-Fermi-liquid characteristic under any electron density. Introducing hole carriers to the half-filled FK model leads to Mott insulator-metal transition, where the Mott quantum criticality manifests unconventional scaling behavior in transport properties. Further insight on the violation of Luttinger's theorem is examined by combining Hubbard-I approximation with a composite fermion picture, which emphasizes the importance of a mixed excitation of the itinerant electron and the composite fermion. Interestingly, comparing the FK model with a binary disorder system suggests that the two-peak band structure discovered by Monte Carlo and Hubbard-I approaches is underlying the violation of Luttinger's theorem.
Abstract The mysterious metallic phase showing T-linear resistivity and a universal scattering rate 1 / τ = α P k B T / ℏ with a universal prefactor α P ∼ 1 and logarithmic-in-temperature singular specific heat coefficient, the so-called ‘Planckian metal phase’ was observed in various overdoped high- T c cuprate superconductors over a finite range in doping. Revealing the mystery of the Planckian metal state is believed to be the key to understanding the mechanism for high- T c superconductivity. Here, we propose a generic microscopic mechanism for this state based on quantum-critical local bosonic charge Kondo fluctuations coupled to both spinon and a heavy conduction-electron Fermi surface within the heavy-fermion formulation of the slave-boson t–J model. By a controlled perturbative renormalization group analysis, we examine the competition between the pseudogap phase, characterized by Anderson’s Resonating-Valence-Bond spin-liquid, and the Fermi-liquid state, modeled by the electron hopping (effective charge Kondo effect). We find a quantum-critical metallic phase with a universal Planckian ℏ ω / k B T scaling in scattering rate near an extended localized-delocalized (pseudogap-to-Fermi liquid) charge-Kondo breakdown transition. The d-wave superconducting ground state emerges near the transition. Unprecedented qualitative and quantitative agreements are reached between our theoretical predictions and various experiments, including optical conductivity, universal doping-independent field-to-temperature scaling in magnetoresistance, specific heat coefficient, marginal Fermi-liquid spectral function observed in ARPES, and Fermi surface reconstruction observed in Hall coefficients in various overdoped cuprates. Our mechanism offers a microscopic understanding of the quantum-critical Planckian metal phase observed in cuprates and its link to the pseudogap, d-wave superconducting, and Fermi liquid phases. It offers a promising route for understanding how d-wave superconductivity emerges from such a strange metal phase in cuprates–one of the long-standing open problems in condensed matter physics since 1990s–as well as shows a broader implication for the Planckian strange metal states observed in other correlated unconventional superconductors.