Traversable wormhole and Hawking-Page transition in coupled complex SYK models

TL;DR

This paper explores coupled complex SYK models with U(1) symmetry, revealing rich phase structures including traversable wormholes, black hole analogs, and phase transitions, with implications for experimental realizations.

Contribution

It generalizes SYK models to include complex fermions with charge symmetry, analyzing their phase diagram and dual gravitational interpretations.

Findings

Identification of a charge-neutral gapped phase supporting revival oscillations.

Discovery of two gapless non-Fermi liquid phases with tunable charge density.

Observation of a first-order Hawking-Page type phase transition.

Abstract

Recent work has shown that coupling two identical Sachdev-Ye-Kitaev (SYK) models can realize a phase of matter that is holographically dual to an eternal traversable wormhole. This phase supports revival oscillations between two quantum chaotic systems that can be interpreted as information traversing the wormhole. Here we generalize these ideas to a pair of coupled SYK models with complex fermions that respect a global U(1) charge symmetry. Such models show richer behavior than conventional SYK models with Majorana fermions and may be easier to realize experimentally. We consider two different couplings, namely tunneling and charge-conserving two-body interactions, and obtain the corresponding phase diagram using a combination of numerical and analytical techniques. At low temperature we find a charge-neutral gapped phase that supports revival oscillations, with a ground state close to the thermofield double, which we argue is dual to a traversable wormhole. We also find two different gapless non-Fermi liquid phases with tunable charge density which we interpret as dual to a `large' and `small' charged black hole. The gapped and gapless phases are separated by a first-order phase transition of the Hawking-Page type. Finally, we discuss an SU(2)-symmetric limit of our model that is closely related to proposed realizations of SYK physics with spinful fermions in graphene, and explain its relevance for future experiments on this system.