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arXiv · 2512.16859

Slow growth of quantum magic in disorder-free Stark many-body localization

Han-Ze Li·Yi-Rui Zhang·Yu-Jun Zhao·Xuyang Huang·Jian-Xin Zhong
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Abstract

Disorder-free quantum many-body localization can strongly suppress transport while still enabling the dynamical buildup of computationally costly non-Clifford resources. In a tilted transverse-field Ising chain realizing disorder-free Stark many-body localization, we use the stabilizer R\'enyi entropy to quantify quantum magic (nonstabilizerness) and find that it remains finite and grows anomalously slowly over extended time windows before saturating to a size-dependent plateau deep in the strong-tilt regime, with pronounced initial-state selectivity. Upon increasing the Stark gradient, the long-time magic and half-chain entanglement exhibit consistent finite-size crossing behavior, indicating a crossover from ergodic dynamics to constrained localization. These results establish stabilizer-based magic as a practical complexity diagnostic of disorder-free ergodicity breaking and constrained dynamics, and provide an experimentally accessible route to benchmarking and designing near-term quantum simulators.

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Han-Ze Li, Yi-Rui Zhang, Yu-Jun Zhao, Xuyang Huang, Jian-Xin Zhong. 2025-12-18. Slow growth of quantum magic in disorder-free Stark many-body localization. https://arxiv.org/abs/2512.16859

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