2016/12/31 by Richard A. Davison, Wenbo Fu, Antoine Georges +3 · 1 citation
Physics and Astronomy · #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.95.155131
published as Phys. Rev. B 95, 155131 (2017) · 57 pages, 6 figures; (v2) clarifications and refs
arxiv created 2017/03/21 · arxiv updated 2017/04/26
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-scalar 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 non-quasiparticle 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.