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arXiv · 2611.00233

Distance to integrability and complexity

Sean Casey·Marius de Leeuw·Tristan McLoughlin·Sergiy Zhuk
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Abstract

We consider nearest-neighbour interactions on spin-1/2 chains. We find the full set of integrable models of this form and apply a numerical algorithm to determine the "closest" integrable model for a given Hamiltonian. This allows us to define a model-independent distance to integrability. We show that standard measures of chaos interpolate between integrable and chaotic values with increasing values of this distance. However, there is a large variation across models and the distance to integrability provides additional information not directly provided by these diagnostics.

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Sean Casey, Marius de Leeuw, Tristan McLoughlin, Sergiy Zhuk. 2026-10-30. Distance to integrability and complexity. https://arxiv.org/abs/2611.00233

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