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arXiv:2610.24208

Kohler's Rule Holds in the Strange Metallic Hubbard Model

Rebekah M. Jin, Emily Z. Zhang, Jixun K. Ding, Brian Moritz, T. P. Devereaux

Published Oct 16, 2026• 0 citations
arXivHTMLPDF

Abstract

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 $T$-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 $T^\star\approx t$ 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.

DOI
10.48550/arxiv.2610.24208

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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.
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.
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Despite much theoretical effort, there is no complete theory of the "strange" metal state of the high temperature superconductors, and its linear-in-temperature T resistivity.Recent experiments showing an unexpected linear-in-field B magnetoresistivity have deepened the puzzle.We propose a simple model of itinerant electrons, interacting via random couplings, with electrons localized on a lattice of "quantum dots" or "islands."This model is solvable in a particular large-N limit and can reproduce observed behavior.The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations.For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-T resistivity and a T ln T specific heat as T → 0. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-T crossover to a fully incoherent regime that also has a linear-in-T resistivity.We describe the magnetotransport properties of this model and show that the MFL regime has conductivities that scale as a function of B=T; however, the magnetoresistance saturates at large B. We then consider a macroscopically disordered sample with domains of such MFLs with varying densities of electrons and islands.Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field B applied perpendicular to the plane of the sample, at large B. The resistance also scales linearly in T at small B, and as TfðB=TÞ at intermediate B. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.
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.
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
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.