Sparsity-Independent Lyapunov Exponent in the Sachdev-Ye-Kitaev Model
The saturation of a recently proposed universal bound on the Lyapunov exponent has been conjectured to signal the existence of a gravity dual. This saturation occurs in the low-temperature limit of the dense Sachdev-Ye-Kitaev (SYK) model, Majorana fermions with body ( ) infinite-range interactions. We calculate certain out-of-time-order correlators (OTOCs) for fermions for a highly sparse SYK model and find no significant dependence of the Lyapunov exponent on sparsity up to near the percolation limit where the Hamiltonian breaks up into blocks. This provides strong support to the saturation of the Lyapunov exponent in the low-temperature limit of the sparse SYK. A key ingredient to reaching is the development of a novel quantum spin model simulation library that implements highly optimized matrix-free Krylov subspace methods on graphical processing units. This leads to a significantly lower simulation time as well as vastly reduced memory usage over previous approaches, while using modest computational resources. Strong sparsity-driven statistical fluctuations require both the use of a much larger number of disorder realizations with respect to the dense limit and a careful finite size scaling analysis. The saturation of the bound in the sparse SYK points to the existence of a gravity analog that would enlarge substantially the number of field theories with this feature.
Published by the American Physical Society 2024- Sponsoring Organization:
- USDOE
- OSTI ID:
- 2437772
- Alternate ID(s):
- OSTI ID: 2579736
- Journal Information:
- Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 9 Vol. 133; ISSN 0031-9007; ISSN PRLTAO
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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