PreprintCC BY 4.0arXiv
Universality and Emergent Classicality in Krylov Space
Abstract
Krylov complexity grows linearly at late times for many systems. In this regime, we give a general spectral formula for the leading growth coefficients of Krylov complexity and its higher moments, without requiring detailed knowledge of the Lanczos coefficients. For states with a narrow energy distribution compared to the bandwidth, dynamics in the Krylov basis resembles motion along a classical trajectory. We demonstrate our results for the critical XY chain and double-scaled SYK. For the latter, we compute the leading late-time behavior of the chord-number moments through one-loop order.
Related
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BibTeX
@misc{chakraborty2026universality,
title = {{Universality and Emergent Classicality in Krylov Space}},
author = {Debarghya Chakraborty},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03188},
eprint = {2611.03188},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03188},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universality and Emergent Classicality in Krylov Space
AU - Debarghya Chakraborty
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03188
UR - https://arxiv.org/abs/2611.03188
AB - Krylov complexity grows linearly at late times for many systems. In this regime, we give a general spectral formula for the leading growth coefficients of Krylov complexity and its higher moments, without requiring detailed knowledge of the Lanczos coefficients. For states with a narrow energy distribution compared to the bandwidth, dynamics in the Krylov basis resembles motion along a classical trajectory. We demonstrate our results for the critical XY chain and double-scaled SYK. For the latter, we compute the leading late-time behavior of the chord-number moments through one-loop order.
ER -