Sparsity dependence of Krylov state complexity in the SYK model
We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for N ≤ 28 Majorana fermions with q -body fermion interaction with q = 4 , 6, 8 for a range of sparse parameter k that controls the number of remaining terms in the original SYK model after sparsification. The critical value o...
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| Published in: | Physical review. D Vol. 112; no. 4 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
American Physical Society (APS)
21.08.2025
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| ISSN: | 2470-0010, 2470-0029, 2470-0029 |
| Online Access: | Get full text |
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| Summary: | We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for N ≤ 28 Majorana fermions with q -body fermion interaction with q = 4 , 6, 8 for a range of sparse parameter k that controls the number of remaining terms in the original SYK model after sparsification. The critical value of k below which the model ceases to be holographic, denoted k c , has been subject of several recent investigations. Using Krylov complexity as a probe, we find that the peak value of complexity does not change as we increase k beyond k ≥ k min at large temperatures. We argue that this behavior is related to the change in the holographic nature of the Hamiltonian in the sparse SYK-type models such that the model is holographic for all k ≥ k min ≈ k c . Our results provide a novel way to determine k c in SYK-type models. |
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| Bibliography: | U.S. Department of Energy JLAB-THY-24-4131; DOE/OR/23177-7578; arXiv:2407.20569 Office of Science Co-design Center for Quantum Advantage AC05-06OR23177; SC0012704 National Quantum Information Science Research Centers |
| ISSN: | 2470-0010 2470-0029 2470-0029 |
| DOI: | 10.1103/qsyk-m3sg |