Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography

We compute the thermodynamic properties of the Sachdev-Ye-Kitaev (SYK) models of fermions with a conserved fermion number Q. We extend a previously proposed Schwarzian effective action to include a phase field, and this describes the low-temperature energy and Q fluctuations. We obtain higher-dimensional generalizations of the SYK models which display disordered metallic states without quasiparticle excitations, and we deduce their thermoelectric transport coefficients. We also examine the corresponding properties of Einstein-Maxwell-axion theories on black brane geometries which interpolate from either AdS4 or AdS5 to an AdS2×R2 or AdS2×R3 near-horizon geometry. These provide holographic descriptions of nonquasiparticle metallic states without momentum conservation. We find a precise match between low-temperature transport and thermodynamics of the SYK and holographic models. In both models, the Seebeck transport coefficient is exactly equal to the Q derivative of the entropy. For the SYK models, quantum chaos, as characterized by the butterfly velocity and the Lyapunov rate, universally determines the thermal diffusivity, but not the charge diffusivity.