Commuting SYK: a pseudo-holographic model

Abstract: In this work, we study a type of commuting SYK model in which all terms in the Hamiltonian are commutative to each other. Because of the commutativity, this model has a large number of conserved charges and is integrable. After the ensemble average of random couplings, we can solve this model exactly in any $N$. Though this integral model is not holographic, we do find that it has some holography-like features, especially the near-perfect size winding in high temperatures. Therefore, we would like to call it pseudo-holographic. We also find that the size winding of this model has a narrowly peaked size distribution, which is different from the ordinary SYK model. We apply the traversable wormhole teleportation protocol in the commuting SYK model and find that the teleportation has a few features similar to the semiclassical traversable wormhole but in different parameter regimes. We show that the underlying physics is not entirely determined by the size-winding mechanism but involves the peaked-size mechanism and thermalization. Lastly, we comment on the recent simulation of the dynamics of traversable wormholes on Google's quantum processor.