A Sparse Model of Quantum Holography

TL;DR

This paper introduces a sparse version of the SYK model on hypergraphs, which retains key holographic and chaotic properties while enabling more efficient numerical and quantum simulations, opening new avenues in quantum gravity research.

Contribution

The paper develops a sparse SYK model on hypergraphs that preserves the physics of the original model and significantly reduces computational complexity.

Findings

Sparse SYK exhibits maximal chaos at low temperatures.

Numerical results align with path integral predictions.

Sparsity reduces quantum simulation costs.

Abstract

We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, $k$, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed $k$. We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when $k$ is of order unity. In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic. Our argument proceeds by constructing a path integral for the sparse model which reproduces the conventional SYK path integral plus gapped fluctuations. The sparsity of the model permits larger scale numerical calculations than previously possible, the results of which are consistent with the path integral analysis. Additionally, we show that the sparsity of the model considerably reduces the cost of quantum simulation algorithms. This makes the sparse SYK model the most efficient currently known route to simulate a holographic model of quantum gravity. We also define and study a sparse supersymmetric SYK model, with similar conclusions to the non-supersymmetric case. Looking forward, we argue that the class of models considered here constitute an interesting and relatively unexplored sparse frontier in quantum many-body physics.