Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography

TL;DR

This paper explores disordered metallic states without quasiparticles using SYK models and holography, revealing universal relations in thermoelectric transport and connections to quantum chaos.

Contribution

It extends SYK models with a phase field, generalizes them to higher dimensions, and establishes a precise holographic duality for non-quasiparticle metallic states.

Findings

Seebeck coefficient equals the Q-derivative of entropy.

Transport properties match between SYK and holographic models.

Quantum chaos universally determines thermal diffusivity.

Abstract

We compute the thermodynamic properties of the Sachdev-Ye-Kitaev (SYK) models of fermions with a conserved fermion number, $\mathcal{Q}$. We extend a previously proposed Schwarzian effective action to include a phase field, and this describes the low temperature energy and $\mathcal{Q}$ 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 AdS$_4$ or AdS$_5$ to an AdS$_2\times \mathbb{R}^2$ or AdS$_2\times \mathbb{R}^3$ 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 $\mathcal{Q}$-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.