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Sub-extensive non-stabilizerness in the Dyck-Fredkin spin chain

  • Yasunori Lee
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Abstract

The stabilizer Rényi entropy is a quantitative measure of non-stabilizerness, or magic, and has typically been found to scale extensively with system size N (i.e., Θ(N)) for a variety of many-body quantum states. In this note, we study the stabilizer Rényi entropy of the ground state of the spin-1/2 Dyck-Fredkin chain and its t-deformation, a local frustration-free model with unusual spectral-gap scaling. Exploiting the combinatorial structure, we carry out numerically exact finite-size calculations, which indicate asymptotic behavior depending on t: Θ(N) for t<1, Θ(log N) at t=1, and Θ(1) for t>1. The scaling at t=1 could be another manifestation of the unconventional criticality of the model, while the contrast with the behavior of the entanglement entropy suggests that non-stabilizerness might provide a new window into quantum many-body systems.

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Cite

BibTeXRIS
BibTeX
@misc{lee2026subextensive,
  title = {{Sub-extensive non-stabilizerness in the Dyck-Fredkin spin chain}},
  author = {Yasunori Lee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09545},
  eprint = {2609.09545},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09545},
}
RIS
TY  - UNPB
TI  - Sub-extensive non-stabilizerness in the Dyck-Fredkin spin chain
AU  - Yasunori Lee
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09545
UR  - https://arxiv.org/abs/2609.09545
AB  - The stabilizer Rényi entropy is a quantitative measure of non-stabilizerness, or magic, and has typically been found to scale extensively with system size N (i.e., Θ(N)) for a variety of many-body quantum states. In this note, we study the stabilizer Rényi entropy of the ground state of the spin-1/2 Dyck-Fredkin chain and its t-deformation, a local frustration-free model with unusual spectral-gap scaling. Exploiting the combinatorial structure, we carry out numerically exact finite-size calculations, which indicate asymptotic behavior depending on t: Θ(N) for t<1, Θ(log N) at t=1, and Θ(1) for t>1. The scaling at t=1 could be another manifestation of the unconventional criticality of the model, while the contrast with the behavior of the entanglement entropy suggests that non-stabilizerness might provide a new window into quantum many-body systems.
ER  -