Krylov complexity in large-$q$ and double-scaled SYK model
High Energy Physics - Theory
2023-08-21 v4 Strongly Correlated Electrons
Quantum Physics
Abstract
Considering the large- expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the effects. The Krylov complexity naturally describes the "size" of the distribution, while the higher cumulants encode richer information. We further consider the double-scaled limit of SYK at infinite temperature, where . In such a limit, we find that the scrambling time shrinks to zero, and the Lanczos coefficients diverge. The growth of Krylov complexity appears to be "hyperfast", which is previously conjectured to be associated with scrambling in de Sitter space.
Cite
@article{arxiv.2210.02474,
title = {Krylov complexity in large-$q$ and double-scaled SYK model},
author = {Budhaditya Bhattacharjee and Pratik Nandy and Tanay Pathak},
journal= {arXiv preprint arXiv:2210.02474},
year = {2023}
}
Comments
v4: minor changes, published version in JHEP