Quantum chaos in the sparse SYK model
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1.
University of California, San Diego
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2.
California Institute of Technology
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3.
University of Alabama at Birmingham
- 4. BlueQubit Inc.
Abstract
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/N 3, 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 < p1, deviations from unsparsified SYK and RMT occur, indicating a breakdown of holography in the highly sparsified regime. Below an even smaller value p2, which also scales as 1/N 3, even the spacing of consecutive eigenvalues differs from RMT values, signaling a complete breakdown of spectral rigidity. Our results cast doubt on the holographic interpretation of very highly sparsified SYK models obtained via machine learning using teleportation infidelity as a loss function.
Copyright and License
© 2025 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3.
Acknowledgement
We are grateful for helpful discussions with Brian Swingle, Stephen Shenker, Masanori Hanada, Douglas Stanford, Juan Maldacena, Sandip Trivedi, Alexey Milekhin, Tommy Schuster, and Alexei Kitaev. The research of PO was supported in part by Caltech’s Summer Undergraduate Research Fellowship (SURF) program. PO also acknowledges the Perimeter Institute for Theoretical Physics, which sponsored a visit enabling him to present this work at the 2023 It from Qubit Conference. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation and Science. HG was supported by the Simons Foundation It from Qubit Collaboration, the Institute for Quantum Information and Matter at Caltech, and BlueQubit Inc. JP acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907), the Simons Foundation It from Qubit Collaboration, the DOE QuantISED program (DE-SC0018407), and the Air Force Office of Scientific Research (FA9550-19-1-0360). Dedicated in memory of “Pop”, Lee R. Summerlin II (1934–2024), whose everlasting impact as a grandfather, mentor, and teacher reach beyond what words can capture.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2403.13884 (arXiv)
Funding
- California Institute of Technology
- Innovation, Science and Economic Development Canada
- Ministry of Research, Innovation and Science
- Simons Foundation
- National Science Foundation
- PHY-1733907
- United States Department of Energy
- DE-SC0018407
- United States Air Force Office of Scientific Research
- FA9550-19-1-0360
- SCOAP3
Dates
- Accepted
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2025-01-13
- Available
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2025-02-26Published