Grand canonical vs. canonical Krylov complexity in double-scaled complex SYK model
Abstract
A bstract 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.
Fields of Study & Subjects
Quantum many-body systems
Physics of Superconductivity and Magnetism
Theoretical and Computational Physics
Publication details
- Journal / source
- Journal of High Energy Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 9
- Publication date
- 1 September 2026
- Language
- EN