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arXiv:1806.08346 · Science

Strange metallicity in the doped Hubbard model

Edwin W. Huang, Ryan Sheppard, Brian Moritz, Thomas Devereaux

Published Nov 22, 2019• 147 citations
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Abstract

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.

DOI
10.1126/science.aau7063

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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.
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
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 UUU limit, first identifying a doping-induced percolation transition in the low-energy sector occurring at a definite critical doping pc{p}_{c}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-NNN model with distinct non-Fermi-liquid properties. We show that this model has linear-in-TTT resistivity with doping-dependent slope maximized at p=pcp={p}_{c}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.
Unconventional magnetotransport violating Kohler's rule has been reported in many strongly correlated strange metals, but the exact origin of these violations is yet unknown. To investigate this question, we use determinant quantum Monte Carlo to compute the magnetoresistance of the hole-doped Hubbard-Hofstadter model. Despite TTT-linear resistivity exceeding the Mott-Ioffe-Regel limit and the nominal absence of well-defined quasiparticles, we find Kohler's rule unexpectedly holds across a wide range of on-site interaction strengths and hole dopings. In particular, Kohler emerges below a crossover temperature T⋆≈tT^\star\approx tT⋆≈t identified from the double occupancy and specific heat, coinciding with the onset of local singlet correlations between lattice sites. We thus propose that Kohler scaling in this regime reflects a more general form of many-body quantum coherence. Our results show that strong correlations and strange metallicity do not themselves generically produce anomalous magnetoresistance.
Strongly correlated metals often display anomalous transport, including T-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for bad metals, by restoring in the well-known Hubbard model-with hopping t and on-site repulsion U-a "screened Coulomb" interaction between charge densities that decays exponentially with spatial separation. This interaction lifts the extensive degeneracy in the spectrum of the t=0 Hubbard model, allowing us to fully characterize the small t electric, thermal, and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe T-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Wiedemann-Franz law and a large thermopower that can undergo sign change.
Bad metals exhibit approximately TTT-linear dc resistivity beyond the Ioffe--Regel limit. That this behavior occurs in systems with radically different ground states suggests it is a generic manifestation of strong local correlations. We test this hypothesis in the infinite-UUU Hubbard model with small hole densities using exact diagonalization to compute thermodynamic and transport properties of finite clusters. Upon cooling, we find an intermediate temperature range, an electronic analogue of the ``semi-quantum regime'' of liquid helium, in which quantum effects produce a roughly TTT-independent compressibility, yet the resistivity is TTT-linear and exceeds the Ioffe--Regel limit. Entry into this regime is accompanied by the formation of quasi-local ferromagnetic ``spin cages'' around doped holes, regions that facilitate local quantum motion embedded in a fluctuating spin background, analogous to the transient crystalline cages thought to control incoherent transport in semi-quantum liquid helium. Remarkably, despite the simplicity of the model, the bad metal behavior found here resembles that seen in various material platforms.
Metallic quantum states coined strange metal (SM), with robust linear-TTT resistivity, have been widely observed in many quantum materials under strong electron correlations, ranging from high-Tc{T}_{c}Tc​ cuprate superconductors and organic superconductors to twisted multilayer graphene and MoTe2/WSe2{\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}MoTe2​/WSe2​ superlattices. Despite decades of intensive studies, the mystery of SM still defies any sensible theoretical explanation and has been a key puzzle in modern condensed matter physics. Here, we solve a doped Mott insulator model called an Ising-Kondo lattice, which includes static spin fluctuation. With Monte Carlo simulation, the Ising-Kondo lattice unambiguously exhibits SM phenomena accompanied with quantum critical scaling in observables, e.g., resistivity, susceptibility, and specific heat. A closer look at SM reveals the breakdown of Landau's Fermi liquid theory without any symmetry breaking, i.e., the violation of Luttinger theorem. Our paper reveals that the long-overlooked static fluctuations in literature may play an essential role in non-Fermi liquid behaviors in correlated electron systems.