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Motivated by the ground state structure of quantum models with all-to-allinteractions such as mean-field quantum spin glass models and theSachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture whichcan accomodate volume law entanglement and a large ground state degeneracy. Wecall this architecture the non-local renormalization ansatz (NoRA) because itcan be viewed as a generalization of MERA, DMERA, and branching MERA networkswith the constraints of spatial locality removed. We argue that thearchitecture is potentially expressive enough to capture the entanglement andcomplexity of the ground space of the SYK model, thus making it a suitablevariational ansatz, but we leave a detailed study of SYK to future work. Wefurther explore the architecture in the special case in which the tensors arerandom Clifford gates. Here the architecture can be viewed as the encoding mapof a random stabilizer code. We introduce a family of codes inspired by the SYKmodel which can be chosen to have constant rate and linear distance at the costof some high weight stabilizers. We also comment on potential similaritiesbetween this code family and the approximate code formed from the SYK groundspace.

NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians