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

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., $\Theta(N)$) 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 $t$: $\Theta(N)$ for $t<1$, $\Theta(\log N)$ at $t=1$, and $\Theta(1)$ 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.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2609.09545 [quant-ph]

(or arXiv:2609.09545v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.09545 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.