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

TL;DR

This paper introduces NoRA, a tensor network architecture capable of representing volume-law entangled states in highly connected Hamiltonians, inspired by models like SYK, and explores its properties and potential applications.

Contribution

The paper proposes NoRA, a non-local tensor network ansatz that generalizes existing models to capture volume-law entanglement in complex quantum systems.

Findings

NoRA can accommodate volume-law entanglement and large ground state degeneracy.

In the special case with random Clifford tensors, NoRA encodes a family of stabilizer codes.

Potential for NoRA to effectively model SYK ground states and related complex quantum states.

Abstract

Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume law entanglement and a large ground state degeneracy. We call this architecture the non-local renormalization ansatz (NoRA) because it can be viewed as a generalization of MERA, DMERA, and branching MERA networks with the constraints of spatial locality removed. We argue that the architecture is potentially expressive enough to capture the entanglement and complexity of the ground space of the SYK model, thus making it a suitable variational ansatz, but we leave a detailed study of SYK to future work. We further explore the architecture in the special case in which the tensors are random Clifford gates. Here the architecture can be viewed as the encoding map of a random stabilizer code. We introduce a family of codes inspired by the SYK model which can be chosen to have constant rate and linear distance at the cost of some high weight stabilizers. We also comment on potential similarities between this code family and the approximate code formed from the SYK ground space.