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.