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This research introduces operator purity as a robust metric to distinguish between chaotic and integrable quantum systems, overcoming the limitations of OTOCs which fail to differentiate them in interacting many-body contexts. By leveraging the Mazur bound, the study provides concrete scaling estimates that clarify the role of locality in integrable charges, supported by numerical simulations on one-dimensional spin chains. These findings advance theoretical frameworks for characterizing quantum information scrambling and thermalization dynamics.
How to distinguish chaos from integrability using OTOC
arXiv:2610.04197v1 Announce Type: new 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.
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.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
arXiv:2610.04197 [quant-ph]
(or arXiv:2610.04197v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.04197 arXiv-issued DOI via DataCite (pending registration)
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