A Sparse Model of Quantum Holography

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.

43+12 pages, 9 figures

References in corpus (18)

• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Fermionic quantum computation
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Toward the first quantum simulation with quantum speedup
• Bekenstein-Hawking Entropy and Strange Metals
• Towards the fast scrambling conjecture
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• Universal Charge Diffusion and the Butterfly Effect
• The complete $1/N$ expansion of a SYK--like tensor model
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Treelike interactions and fast scrambling with cold atoms
• Quantum Simulation of the Sachdev-Ye-Kitaev Model by Asymmetric Qubitization
• Fast scrambling on sparse graphs
• Does the SYK model have a spin glass phase?
• Scrambling speed of random quantum circuits
• Spectral gap in random bipartite biregular graphs and applications

Cited by in corpus (11)

• Krylov Localization and suppression of complexity
• Wormholes without averaging
• Optimizing sparse fermionic Hamiltonians
• Chaos on the hypercube
• Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs
• Variational wavefunctions for Sachdev-Ye-Kitaev models
• Scrambling in Yang-Mills
• Approximate Quantum Codes From Long Wormholes
• Quantum Annealing with chaotic driver Hamiltonians
• Sparse SYK and traversable wormholes
• Electric Forces in the Charged SYK Model