Grand Canonical vs Canonical Krylov Complexity in Double-Scaled Complex SYK Model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908698376404992 |
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| author | Forste, Stefan Kruse, Yannic Natu, Saurabh |
| author_facet | Forste, Stefan Kruse, Yannic Natu, Saurabh |
| contents | We consider the complex SYK model in the double-scaling limit. We obtain the transfer matrix for the grand canonical ensemble and symmetrize it. In the (n,Q)- basis of chord states, the grand canonical transfer matrix is block diagonal, where each block is the canonical transfer matrix for the respective charge sector. We therefore conclude that the Krylov complexity for the grand canonical ensemble is given by the sum of the complexities in the charge sectors weighted by a probability function that depends on the chemical potential. Finally, we compute the Krylov complexity analytically in the limit of early and late time in the charge sector and numerically for both canonical and grand canonical ensemble. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Grand Canonical vs Canonical Krylov Complexity in Double-Scaled Complex SYK Model Forste, Stefan Kruse, Yannic Natu, Saurabh High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics We consider the complex SYK model in the double-scaling limit. We obtain the transfer matrix for the grand canonical ensemble and symmetrize it. In the (n,Q)- basis of chord states, the grand canonical transfer matrix is block diagonal, where each block is the canonical transfer matrix for the respective charge sector. We therefore conclude that the Krylov complexity for the grand canonical ensemble is given by the sum of the complexities in the charge sectors weighted by a probability function that depends on the chemical potential. Finally, we compute the Krylov complexity analytically in the limit of early and late time in the charge sector and numerically for both canonical and grand canonical ensemble. |
| title | Grand Canonical vs Canonical Krylov Complexity in Double-Scaled Complex SYK Model |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2512.07715 |