PreprintCC0arXiv
How to distinguish chaos from integrability using OTOC
Abstract
The decay of out-of-time-ordered correlators (OTOCs) to a small residual value signals the scrambling of quantum information. This behavior is generic: it occurs in both chaotic and interacting integrable many-body systems, and therefore cannot by itself distinguish between them. In this paper we analytically study the late-time saturation value of a closely related observable, operator purity, and show that its scaling with system size robustly distinguishes chaotic from integrable systems. Our approach is based on the Mazur bound, which provides concrete scaling estimates and makes explicit why the locality of integrable charges matters. We support our findings with numerical simulations of one-dimensional spin chains.
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BibTeX
@misc{milekhin2026distinguish,
title = {{How to distinguish chaos from integrability using OTOC}},
author = {Alexey Milekhin and Anders Wallberg},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04197},
eprint = {2610.04197},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04197},
note = {CC0},
}
RIS
TY - UNPB
TI - How to distinguish chaos from integrability using OTOC
AU - Alexey Milekhin
AU - Anders Wallberg
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04197
UR - https://arxiv.org/abs/2610.04197
AB - The decay of out-of-time-ordered correlators (OTOCs) to a small residual value signals the scrambling of quantum information. This behavior is generic: it occurs in both chaotic and interacting integrable many-body systems, and therefore cannot by itself distinguish between them. In this paper we analytically study the late-time saturation value of a closely related observable, operator purity, and show that its scaling with system size robustly distinguishes chaotic from integrable systems. Our approach is based on the Mazur bound, which provides concrete scaling estimates and makes explicit why the locality of integrable charges matters. We support our findings with numerical simulations of one-dimensional spin chains.
ER -