Sparsity dependence of Krylov state complexity in the SYK model
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| Format: | Preprint |
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2024
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| _version_ | 1866908497682104320 |
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| author | Jha, Raghav G. Roy, Ranadeep |
| author_facet | Jha, Raghav G. Roy, Ranadeep |
| contents | We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for $N \le 28$ 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 $k \ge k_{\text{min}}$ 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 $k \ge k_{\text{min}} \approx k_c$. Our results provide a novel way to determine $k_c$ in SYK-type models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_20569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparsity dependence of Krylov state complexity in the SYK model Jha, Raghav G. Roy, Ranadeep High Energy Physics - Theory High Energy Physics - Lattice Quantum Physics We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for $N \le 28$ 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 $k \ge k_{\text{min}}$ 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 $k \ge k_{\text{min}} \approx k_c$. Our results provide a novel way to determine $k_c$ in SYK-type models. |
| title | Sparsity dependence of Krylov state complexity in the SYK model |
| topic | High Energy Physics - Theory High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2407.20569 |