2024/03/20 by Patrick Orman, Orman, Patrick, Hrant Gharibyan +3 · 7 citations
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2403.13884
openalex publication_date 2024/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Sachdev-Ye-Kitaev (SYK) model is a system of N Majorana fermions with random interactions and strongly chaotic dynamics, which at low energy admits a holographically dual description as two-dimensional Jackiw-Teitelboim gravity. Hence the SYK model provides a toy model of quantum gravity that might be feasible to simulate with near-term quantum hardware. Motivated by the goal of reducing the resources needed for such a simulation, we study a sparsified version of the SYK model, in which interaction terms are deleted with probability 1-p. Specifically, we compute numerically the spectral form factor (SFF, the Fourier transform of the Hamiltonian's eigenvalue pair correlation function) and the nearest-neighbor eigenvalue gap ratio r (characterizing the distribution of gaps between consecutive eigenvalues). We find that when p is greater than a transition value p1, which scales as 1/N3, both the SFF and r match the values attained by the full unsparsified model and with expectations from random matrix theory (RMT). But for p