Abstract
We compute the thermodynamic properties of the Sachdev-Ye-Kitaev (SYK) models of fermions with a conserved fermion number . We extend a previously proposed Schwarzian effective action to include a phase field, and this describes the low-temperature energy and 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 or to an or 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 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.
- Received 14 December 2016
- Revised 17 February 2017
DOI:https://doi.org/10.1103/PhysRevB.95.155131
©2017 American Physical Society
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Physical Review B 50th Anniversary Milestones
These Milestone studies represent lasting contributions to physics by way of reporting significant discoveries, initiating new areas of research, or substantially enhancing the conceptual tools for making progress in the burgeoning field of condensed matter physics.