English

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