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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Symmetry-resolved Krylov complexity and the uncoloured tensor model

  • Shaliya Kotta1
  • P. N. Bala Subramanian1
  1. 1National Institute of Technology Calicut
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Abstract

A bstract : The symmetry-resolved Krylov complexity is a useful tool for studying the chaotic properties of systems endowed with symmetries. We investigate the conditions under which an invariant Hermitian operator would have the symmetry-resolved Krylov complexity in a charge subspace identical to the Krylov complexity of the full operator, and find a necessary and sufficient condition that ensures this matching at all temperatures. Further, we study the Krylov complexity of the Uncoloured Tensor Model, a disorder-free kin of the SYK Model, which has a plethora of symmetries. We identify charge subspaces of the same operator in which equipartition holds, as well as those where it doesn’t, along with observations on the underlying mechanism behind these. We also find that, within the computational limits, the Krylov complexity, averaged over the symmetry subspace, is bounded above by that of the operator in the full space.

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Cite

BibTeXRIS
BibTeX
@article{kotta2026symmetryresolved,
  title = {{Symmetry-resolved Krylov complexity and the uncoloured tensor model}},
  author = {Shaliya Kotta and P. N. Bala Subramanian},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)042},
  url = {https://link.springer.com/10.1007/JHEP10(2026)042},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Symmetry-resolved Krylov complexity and the uncoloured tensor model
AU  - Shaliya Kotta
AU  - P. N. Bala Subramanian
PY  - 2026
DA  - 2026/10/05
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)042
UR  - https://link.springer.com/10.1007/JHEP10(2026)042
AB  - A bstract : The symmetry-resolved Krylov complexity is a useful tool for studying the chaotic properties of systems endowed with symmetries. We investigate the conditions under which an invariant Hermitian operator would have the symmetry-resolved Krylov complexity in a charge subspace identical to the Krylov complexity of the full operator, and find a necessary and sufficient condition that ensures this matching at all temperatures. Further, we study the Krylov complexity of the Uncoloured Tensor Model, a disorder-free kin of the SYK Model, which has a plethora of symmetries. We identify charge subspaces of the same operator in which equipartition holds, as well as those where it doesn’t, along with observations on the underlying mechanism behind these. We also find that, within the computational limits, the Krylov complexity, averaged over the symmetry subspace, is bounded above by that of the operator in the full space.
SN  - 1029-8479
ER  -