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arXiv:2407.21102 · Physical Review Letters

Enhanced Strange Metallicity due to Hubbard- U Coulomb Repulsion

Andrew Hardy, Olivier Parcollet, Antoine Georges, Aavishkar A. Patel

Published Jan 23, 2025• 10 citations
arXivHTMLPDF

Abstract

We solve a model of electrons with Hubbard-U Coulomb repulsion and a random Yukawa coupling to a two-dimensional bosonic bath, using an extended dynamical mean field theory scheme. Our model exhibits a quantum critical point, at which the repulsive component of the electron interactions strongly enhances the effects of the quantum critical bosonic fluctuations on the electrons, leading to a breakdown of Fermi liquid physics and the formation of a strange metal with "Planckian" [O(k_{B}T/ℏ)] quasiparticle decay rates at low temperatures T→0. Furthermore, the eventual Mott transition that occurs as the repulsion is increased seemingly bounds the maximum decay rate in the strange metal. Our results provide insight into low-temperature strange metallicity observed in proximity to a Mott transition, as is observed, for instance, in recent experiments on certain moiré materials.

DOI
10.1103/physrevlett.134.036502

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We solve a model of electrons with Hubbard-U Coulomb repulsion and a random Yukawa coupling to a two-dimensional bosonic bath, using an extended dynamical mean field theory scheme. Our model exhibits a quantum critical point, at which the repulsive component of the electron interactions strongly enhances the effects of the quantum critical bosonic fluctuations on the electrons, leading to a breakdown of Fermi liquid physics and the formation of a strange metal with "Planckian" [O(k_{B}T/ℏ)] quasiparticle decay rates at low temperatures T→0. Furthermore, the eventual Mott transition that occurs as the repulsion is increased seemingly bounds the maximum decay rate in the strange metal. Our results provide insight into low-temperature strange metallicity observed in proximity to a Mott transition, as is observed, for instance, in recent experiments on certain moiré materials.
Strange metals—ubiquitous in correlated quantum materials—transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures ( T ), such metals generically exhibit strange metal behavior with a T -linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/ T ) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.
The strange metal phase of correlated electrons materials was described in a recent theory by a model of a Fermi surface coupled a two-dimensional quantum critical bosonic field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal were obtained for a wide range of intermediate temperatures, including the linear in temperature resistivity. The Harris criterion implies that spatial fluctuations in the local position of the critical point must dominate at lower temperatures. For an [Formula: see text]-component boson with [Formula: see text], we use multiple graphics processing units (GPUs) to compute the real frequency spectrum of the boson propagator in a self-consistent mean-field treatment of the boson self-interactions, but an exact treatment of multiple realizations of the spatial randomness from the random boson mass. We find that Landau damping from the fermions leads to the emergence of the physics of the random transverse-field Ising model at low temperatures, as has been proposed by Hoyos, Kotabage, and Vojta. This regime is controlled by localized overdamped eigenmodes of the bosonic scalar field, also has a resistivity which is nearly linear-in-temperature, and extends into a "quantum critical phase" away from the quantum critical point, as observed in several cuprates. For the [Formula: see text] Ising scalar, the mean-field treatment is not applicable, and so we use Hybrid Monte Carlo simulations running on multiple GPUs; we find a rounded transition and localization physics, with strange metal behavior in an extended region around the transition.
The gas-liquid transition is a first-order transition terminating at a finite-temperature critical point with diverging density fluctuations. Mott transition, a metal-insulator transition driven by Coulomb repulsion between electrons, has been identified with this textbook transition. However, the critical temperature of the Mott transition can be suppressed, resulting in unusual quantum criticality. It accounts for non-Fermi-liquid-like properties, and strongly momentum dependent quasiparticles as in many materials near the Mott insulator. Among all, the mode-coupling theory of the density fluctuations supports d-wave superconductivity at the order of a hundred Kelvin for relevant parameters of the copper oxide superconductors.
Resilient strange metal at an unconventional quantum critical point in d=2d=2d=2
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→0T\rightarrow{0}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.
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.
The authors introduce exactly solvable models of the quantum phase transition, marking the breakdown of the heavy Fermi liquid in heavy-fermion materials. The solutions capture the puzzling non-Fermi liquid transport with linear-in-temperature resistivity, as seen in experiments. Furthermore, they reveal a broad regime in which a ``Planckian'' strange metal is established, namely the quasiparticle lifetime in this regime is set only by fundamental constants and the temperature. The new large-NNN approach introduced in the paper may be useful for describing a broader class of quantum critical points in systems with strong electronic correlations.