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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 eternaltraversable wormhole. This phase supports revival oscillations between twoquantum chaotic systems that can be interpreted as information traversing thewormhole. Here we generalize these ideas to a pair of coupled SYK models withcomplex fermions that respect a global U(1) charge symmetry. Such models showricher behavior than conventional SYK models with Majorana fermions and may beeasier to realize experimentally. We consider two different couplings, namelytunneling and charge-conserving two-body interactions, and obtain thecorresponding phase diagram using a combination of numerical and analyticaltechniques. At low temperature we find a charge-neutral gapped phase thatsupports revival oscillations, with a ground state close to the thermofielddouble, which we argue is dual to a traversable wormhole. We also find twodifferent gapless non-Fermi liquid phases with tunable charge density which weinterpret as dual to a `large' and `small' charged black hole. The gapped andgapless phases are separated by a first-order phase transition of theHawking-Page type. Finally, we discuss an SU(2)-symmetric limit of our modelthat is closely related to proposed realizations of SYK physics with spinfulfermions in graphene, and explain its relevance for future experiments on thissystem.

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