Quantum chaos and late-time equipartition of symmetry-resolved Krylov complexity
Abstract
We study symmetry-resolved Krylov complexity in finite-dimensional chaotic quantum many-body systems. When both the Hamiltonian and the initial operator commute with a conserved charge, the operator dynamics decomposes into independent symmetry sectors, each with its own Krylov chain. We show that, after saturation, the unresolved Krylov complexity is additive over symmetry sectors. In the absence of additional Liouvillian degeneracies, the late-time contribution of a sector with Hilbert-space dimension dq is controlled by dq(dq−1), leading to a dimension-weighted equipartition that approaches the simple large-sector scaling dq2/∑q'dq'2. This late-time rule differs from the early-time weighted-average discussed in the literature and is governed instead by the dimensions of the accessible operator spaces. We support the analytic prediction with numerical studies of the real and complex SYK models, a chaotic bosonic spin model, and the mixed-field Ising chain. Our results show that resolving exact symmetries is essential for interpreting the saturation value of Krylov complexity as a diagnostic of chaotic operator growth.
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BibTeX
@misc{das2026quantum,
title = {{Quantum chaos and late-time equipartition of symmetry-resolved Krylov complexity}},
author = {Jayashish Das and Suman Das and Juan F. Pedraza and Le-Chen Qu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.19346},
eprint = {2608.19346},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19346},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum chaos and late-time equipartition of symmetry-resolved Krylov complexity
AU - Jayashish Das
AU - Suman Das
AU - Juan F. Pedraza
AU - Le-Chen Qu
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.19346
UR - https://arxiv.org/abs/2608.19346
AB - We study symmetry-resolved Krylov complexity in finite-dimensional chaotic quantum many-body systems. When both the Hamiltonian and the initial operator commute with a conserved charge, the operator dynamics decomposes into independent symmetry sectors, each with its own Krylov chain. We show that, after saturation, the unresolved Krylov complexity is additive over symmetry sectors. In the absence of additional Liouvillian degeneracies, the late-time contribution of a sector with Hilbert-space dimension d_q is controlled by d_q(d_q−1), leading to a dimension-weighted equipartition that approaches the simple large-sector scaling d_q^2/∑_q'd_q'^2. This late-time rule differs from the early-time weighted-average discussed in the literature and is governed instead by the dimensions of the accessible operator spaces. We support the analytic prediction with numerical studies of the real and complex SYK models, a chaotic bosonic spin model, and the mixed-field Ising chain. Our results show that resolving exact symmetries is essential for interpreting the saturation value of Krylov complexity as a diagnostic of chaotic operator growth.
ER -