2025/12/08 by Stefan Forste, Yannic Kruse, Forste, Stefan +3
Physics and Astronomy · #Block (permutation group theory) #Canonical ensemble #Canonical form #Charge (physics) #Grand canonical ensemble #Matrix (chemical analysis) #Microcanonical ensemble #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #Transfer (computing)
paper · pdf · open access · doi:10.48550/arxiv.2512.07715
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
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.