The shared universality of charged black holes and the many many-body SYK model

TL;DR

This paper explores the phase transitions in a charged SYK model and draws parallels with charged black hole phenomena, revealing shared critical behaviors and suggesting a deep connection between many-body quantum systems and gravitational physics.

Contribution

It analytically uncovers the phase diagram of the charged SYK model at large q and establishes its universal features with charged AdS black hole transitions.

Findings

Identifies a phase transition between low and high entropy regimes in the SYK model.

Shows the zero-temperature transition corresponds to a gravitational Hawking-Page transition.

Finds shared critical exponents with charged AdS black hole phase transitions.

Abstract

We investigate the charged $q/2$-body interacting Sachdev-Ye-Kitaev (SYK) model in the grand-canonical ensemble. By treating $q$ as a large parameter, we are able to analytically study its phase diagram. By varying the chemical potential or temperature, we find that the system undergoes a phase transition between low and high entropies, in the maximally chaotic regime. A similar transition in entropy is seen in charged AdS black holes transitioning between a large and small event horizon. Approaching zero temperature, we find a first-order chaotic-to-non-chaotic quantum phase transition, where the finite extensive entropy drops to zero. This again has a gravitational analogue -- the Hawking-Page (HP) transition between a large black hole and thermal radiation. An analytical study of the critical phenomena associated with the continuous phase transition provides us with mean field van der Waals critical and effective exponents. We find that all analogous power laws are shared with several charged AdS black hole phase transitions. Together, these findings indicate a connection between the charged $q\to\infty$ SYK model and black holes.