Fermionic magic resources in disordered quantum spin chains

Abstract:Fermionic non-Gaussianity quantifies a quantum state's deviation from a classically tractable free-fermionic description, constituting a necessary resource for computational quantum advantage. Here we use fermionic antiflatness (FAF) to measure this deviation across ergodic and many-body localized (MBL) regimes. We focus on the paradigmatic disordered spin-$1\!/2$ XXZ chain and its impurity variant with local interactions. Across highly excited eigenstates, FAF evolves from typical-state behavior at weak disorder to strongly suppressed values deep in the MBL regime, with volume-law scaling in the XXZ chain and an area-law bound in the impurity setting. Rare long-range cat-like eigenstates exhibit a pronounced enhancement of FAF, making it a sensitive diagnostic of mechanisms proposed to destabilize MBL. Starting from product states, we find that in the MBL regime FAF grows slowly in time, approaching saturation via a power-law relaxation. Overall, our results show that MBL suppresses fermionic non-Gaussianity, and the associated complexity beyond free fermions, while ergodicity restores it, motivating explorations of fermionic non-Gaussianity in other ergodicity-breaking phenomena.

7 pages of main text + 13 pages of Supplementary Material. 17 Figures. Comments are welcome!

Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)

arXiv:2602.00245 [quant-ph]

(or arXiv:2602.00245v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2602.00245 Focus to learn more arXiv-issued DOI via DataCite

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