Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-$1/2$ fermions

Abstract

`Strange metals' with resistivity depending linearly on temperature $T$ down to low-$T$ have been a long-standing puzzle in condensed matter physics. Here, we consider a model of itinerant spin-$1/2$ fermions interacting via on-site Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behaviour, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-$M$ limit of $SU(M)$ symmetric models, to models with physical $SU(2)$ spin-$1/2$ electrons. Remarkably, the quantum critical regime also features a Planckian linear-$T$ resistivity associated with a $T$-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the Marginal Fermi Liquid phenomenology.

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• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Quantum phases driven by strong correlations
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• Linear-in temperature resistivity from an isotropic Planckian scattering rate
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• Dynamical Mean Field Theory of Moiré Bilayer Transition Metal Dichalcogenides: Phase Diagram, Resistivity, and Quantum Criticality
• Non-Fermi liquid phase and linear-in-temperature scattering rate in overdoped two dimensional Hubbard model
• Traversable wormhole and Hawking-Page transition in coupled complex SYK models
• Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model
• Skewed Non-Fermi Liquids and the Seebeck Effect
• Planckian Metal at a Doping-Induced Quantum Critical Point
• Quantum phase transition at non-zero doping in a random $t$-$J$ model
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