Non-perturbative saturation of Krylov complexity, and its implications in quantum gravity
High Energy Physics - Theory
2026-07-15 v1 Mathematical Physics
Quantum Physics
Abstract
We study the dynamics of Krylov state complexity in finite-dimensional quantum systems. Orthogonal polynomials built on a discrete energy spectrum crowd away from regions where the density of states is low at large Krylov index. The physical implication of this result is that, even using a minimalist Krylov state complexity which is defined over the entire spectrum, the Krylov complexity provably stops growing a little past the Heisenberg length in every low-energy state. This has interesting implications for the proposal that Krylov complexity is related to the wormhole length in 2D quantum gravity.
Keywords
Cite
@article{arxiv.2607.14220,
title = {Non-perturbative saturation of Krylov complexity, and its implications in quantum gravity},
author = {Andrew Lucas and Amit Vikram},
journal= {arXiv preprint arXiv:2607.14220},
year = {2026}
}
Comments
13+8 pages, 1 figure