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arXiv:2606.12665

Hall conductivity reveals the nature of quantum coherence in strongly correlated metals

Emily Z. Zhang, Thomas Devereaux

Published Jun 10, 2026• 0 citations
arXivHTMLPDF

Abstract

Linear-in-temperature resistivity is a hallmark for strange metallic transport, and appears universally in many strongly correlated electron systems. However, the focus on the longitudinal channel often overshadows the profound microscopic insights contained within the transverse response. Here, we utilize numerically exact determinantal quantum Monte Carlo simulations of the doped Hubbard model in a magnetic field to calculate longitudinal and transverse transport. We demonstrate that while the resistivity is robustly $T$-linear across parameter sets, the Hall response is highly sensitive to particle-hole asymmetry, Fermi surface topology, and many-body correlation effects. Specifically, the combination of these effects determine a crossover scale in which the system becomes quantum-coherent, and is reflected in the Hall conductivity. Our results demonstrate that while the $T$-linearity in resistivity appears universal, the Hall response reveals a crossover from semi-classical to quantum-coherent transport otherwise masked in the longitudinal channel.

DOI
10.48550/arxiv.2606.12665

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Linear-in-temperature resistivity is a hallmark for strange metallic transport, and appears universally in many strongly correlated electron systems. However, the focus on the longitudinal channel often overshadows the profound microscopic insights contained within the transverse response. Here, we utilize numerically exact determinantal quantum Monte Carlo simulations of the doped Hubbard model in a magnetic field to calculate longitudinal and transverse transport. We demonstrate that while the resistivity is robustly TTT-linear across parameter sets, the Hall response is highly sensitive to particle-hole asymmetry, Fermi surface topology, and many-body correlation effects. Specifically, the combination of these effects determine a crossover scale in which the system becomes quantum-coherent, and is reflected in the Hall conductivity. Our results demonstrate that while the TTT-linearity in resistivity appears universal, the Hall response reveals a crossover from semi-classical to quantum-coherent transport otherwise masked in the longitudinal channel.
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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Using two approaches to strongly correlated systems, the extremely correlated Fermi liquid theory and the dynamical mean field theory, we compute the transverse transport coefficients, namely, the Hall constants RH{R}_{H}RH​ and Hall angles ${\ensuremath{\theta}}_{H}$, and the longitudinal and transverse optical response of the $U=\ensuremath{\infty}$ Hubbard model in the limit of infinite dimensions. We focus on two successive low-temperature regimes, the Gutzwiller-correlated Fermi liquid (GCFL) and the Gutzwiller-correlated strange metal (GCSM). We find that the Hall angle $cot{\ensuremath{\theta}}_{H}$ is proportional to T2{T}^{2}T2 in the GCFL regime, while upon warming into the GCSM regime it first passes through a downward bend and then continues as T2{T}^{2}T2. Equivalently, RH{R}_{H}RH​ is weakly temperature dependent in the GCFL regime, but becomes strongly temperature dependent in the GCSM regime. Drude peaks are found for both the longitudinal optical conductivity ${\ensuremath{\sigma}}_{xx}(\ensuremath{\omega})$ and the optical Hall angles $tan{\ensuremath{\theta}}_{H}(\ensuremath{\omega})$ below certain characteristic energy scales. By comparing the relaxation rates extracted from fitting to the Drude formula, we find that in the GCFL regime there is a single relaxation rate controlling both longitudinal and transverse transport, while in the GCSM regime two different relaxation rates emerge. We trace the origin of this behavior to the dynamical particle-hole asymmetry of the Dyson self-energy, arguably a generic feature of doped Mott insulators.
Using determinant quantum Monte Carlo simulations, we compare charge transport in the two-dimensional attractive and repulsive Hubbard models at strong coupling, ∣U∣/t=6|U|/t=6∣U∣/t=6. Although the interaction with opposite signs generates qualitatively different low-energy spin, charge, and pairing correlations, both exhibit approximately linear-in-temperature resistivity over a broad intermediate- and high-temperature regime. At asymptotically high temperature this common behavior follows from the moment expansion of the conductivity, whose leading contribution is even in UUU. More strikingly, the similarity persists to temperatures well below ∣U∣|U|∣U∣, where strong interaction-dependent correlations have already developed, and also irrespective of whether resistivity crosses the MIR limit. Using the Nernst--Einstein relation, we find that the common linear-in-temperature resistivity is primarily associated with an approximately Curie-like charge compressibility and weakly temperature-dependent diffusivity. The two models separate only at lower temperatures, where the attractive model develops a pronounced feature in the charge diffusivity correlated with signatures of pair formation. These results show that linear-in-temperature incoherent transport in the Hubbard model can be remarkably insensitive to the microscopic nature of the low-energy correlations. Our results suggest that transport in the incoherent regime appears insensitive to what the system will ultimately become at low temperature; the distinction between competing low-energy states becomes visible only when their characteristic correlations acquire sufficiently long spatial or temporal coherence.