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`Strange metals' with resistivity depending linearly on temperature $T$ downto 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-siteHubbard interaction and random infinite-ranged spin-spin interaction. We showthat the quantum critical point associated with the melting of the spin-glassphase by charge fluctuations displays non-Fermi liquid behaviour, with localspin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. Thisextends the quantum spin liquid dynamics previously established in thelarge-$M$ limit of $SU(M)$ symmetric models, to models with physical $SU(2)$spin-$1/2$ electrons. Remarkably, the quantum critical regime also features aPlanckian linear-$T$ resistivity associated with a $T$-linear scattering rateand a frequency dependence of the electronic self-energy consistent with theMarginal Fermi Liquid phenomenology.

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