Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behaviour in a quantum critical metal with spin-1/2 fermions
Résumé
“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 lattice model of itinerant spin-$1/2$ fermions interacting via onsite 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 behavior, 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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