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A Sparse Model of Quantum Holography
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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.
Forward citations
Cited by 7 Pith papers
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Sharp Bounds on Ground State Energy of the SYK Model
For super-constant k = o(√n), the expected operator norm of the k-SYK Hamiltonian equals (1−o(1))√(2n)/k, via a twisted-boson operator whose moments match SYK trace moments exactly.
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Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy
A generalized latent-entropy measure orders k-uniform states, maxes out on AME states, shows odd-party random states saturate it, and distinguishes SYK variants.
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Entanglement production in the Sachdev-Ye-Kitaev Model and its variants
Entanglement production rates distinguish the spin-SYK model from fermionic SYK and binary SYK, and the differences only become visible at larger system sizes.
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L\'evy Sachdev-Ye-Kitaev Model
In the Lévy-disordered SYK model, spectral correlations crossover from random-matrix (chaotic) to integrable behavior at a disorder strength μ_c that shrinks as N^{-1} (short range) and N^{-1.63} (long range).
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Boosting quantum efficiency by reducing complexity
Sparsifying the SYK quantum battery Hamiltonian improves its charging efficiency (extractable work per stored energy) as long as chaos survives, by up to roughly 10% at N=10.
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Unsupervised Techniques to Detect Quantum Chaos
A self-organizing map fed with raw Hamiltonian matrices responds along the same rewiring-probability axis where spectral r-ratios show a Poisson-to-GUE crossover, though the response may reflect graph geometry instead...
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