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

• URL: http://arxiv.org/abs/2609.09545v1
• Date: Wed, 09 Sep 2026 00:00:00 GMT
• Title: Sub-extensive non-stabilizerness in the Dyck-Fredkin spin chain
• Abstract summary: We study the stabilizer Rényi entropy of the ground state of the spin-$frac12 Dyck-Fredkin chain.<n>We find that the scaling at $t=1$ could be another manifestation of the unconventional criticality of the model.<n>The contrast with the behavior of the entanglement entropy suggests that non-stabilizerness might provide a new window into quantum many-body systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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-$\frac{1}{2}$ 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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