Nonlocal Magic across the Many-Body Localization Crossover

Abstract:Nonlocal magic quantifies the minimum nonstabilizerness attainable under independent local unitary transformations on the two subsystems. Here, we use min-relative nonlocal magic (NLM) to characterize the crossover from ergodicity to many-body localization (MBL) in the random-field XXZ chain. Unlike entanglement entropy, NLM probes how entanglement is organized through the distance of the Schmidt spectrum from dyadic-flat stabilizer spectra. From weak to intermediate disorder, NLM evolves from an $O(1)$ Haar-like value into a size-enhanced dome, while entanglement remains volume-law, revealing a spectral reorganization not visible in the entropy. Deep in the MBL regime, a two-level cut-hybridization model captures the nearly binary Schmidt spectrum and explains why the mean and median NLM decay approximately as $W^{-1}$ and $W^{-2}$, respectively. Following a product-state quench, NLM overshoots and relaxes in the ergodic regime, whereas at strong disorder it grows slowly and approximately logarithmically. These results show that NLM resolves Schmidt-spectrum structure not visible in the entanglement entropy and provides a complementary probe of ergodicity breaking.

6+9.5 pages,5+4 figures

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

arXiv:2609.16935 [cond-mat.dis-nn]

(or arXiv:2609.16935v1 [cond-mat.dis-nn] for this version)

https://doi.org/10.48550/arXiv.2609.16935 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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