Sparse SYK and traversable wormholes

TL;DR

This paper studies sparse SYK models coupled as traversable wormholes, demonstrating their gapped nature, near thermofield double ground states, and signal transmission properties consistent with holographic predictions, using advanced simulation techniques.

Contribution

It introduces a sparse SYK model framework with hypergraph-based sparseness, analyzes its holographic properties, and performs large-scale simulations to explore traversable wormhole behavior.

Findings

Sparse SYK models are gapped with near thermofield double ground states.

Signal transmission between systems exhibits holographic scaling.

Sparsity allows larger system sizes for simulation than all-to-all models.

Abstract

We investigate two sparse Sachdev-Ye-Kitaev (SYK) systems coupled by a bilinear term as a holographic quantum mechanical description of an eternal traversable wormhole in the low temperature limit. Each SYK system consists of $N$ Majorana fermions coupled by random $q$-body interactions. The degree of sparseness is captured by a regular hypergraph in such a way that the Hamiltonian contains exactly $k\,N$ independent terms. We improve on the theoretical understanding of the sparseness property by using known measures of hypergraph expansion. We show that the sparse version of the two coupled SYK model is gapped with a ground state close to a thermofield double state. Using Krylov subspace and parallelization techniques, we simulate the system for $q=4$ and $q=8.$ The sparsity of the model allows us to explore larger values of $N$ than the ones existing in the literature for the all-to-all SYK. We analyze in detail the two-point functions and the transmission amplitude of signals between the two systems. We identify a range of parameters where revivals obey the scaling predicted by holography and signals can be interpreted as traversing the wormhole.