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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{casey2026distance,
  title = {{Distance to integrability and complexity}},
  author = {Sean Casey and Marius de Leeuw and Tristan McLoughlin and Sergiy Zhuk},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00233},
  eprint = {2611.00233},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00233},
}
RIS
TY  - UNPB
TI  - Distance to integrability and complexity
AU  - Sean Casey
AU  - Marius de Leeuw
AU  - Tristan McLoughlin
AU  - Sergiy Zhuk
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00233
UR  - https://arxiv.org/abs/2611.00233
AB  - 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.
ER  -