Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments

TL;DR

This paper explores how thermoelectric measurements in SYK model systems can directly probe the Bekenstein-Hawking entropy, linking quantum matter experiments to black hole physics.

Contribution

It demonstrates that thermopower measurements in SYK-like experimental setups can serve as a direct probe of the system's zero-temperature entropy $S_0$, connecting quantum matter and gravitational theories.

Findings

Thermopower can reveal the zero-temperature entropy $S_0$.

Identifies low-temperature crossovers from SYK criticality to other regimes.

Provides a method to experimentally probe black hole entropy analogs.

Abstract

The Sachdev-Ye-Kitaev (SYK) model describes electrons with random and all-to-all interactions, and realizes a many-body state without quasiparticle excitations, and a non-vanishing extensive entropy $S_0$ in the zero temperature limit. Its low energy theory coincides the low energy theory of the near-extremal charged black holes with Bekenstein-Hawking entropy $S_0$. Several mesoscopic experimental configurations realizing SYK quantum dynamics over a significant intermediate temperature scale have been proposed. We investigate quantum thermoelectric transport in such configurations, and describe the low temperature crossovers out of SYK criticality into regimes with either Fermi liquid behavior, a Coulomb blockade, or criticality associated with Schwarzian quantum gravity fluctuations. Our results show that thermopower measurements can serve as a direct probe for $S_0$.