Nonstabilizerness in Stark many-body localization

Abstract: Quantum many-body disorder-free localization can suppress transport while still allowing the buildup of computationally costly non-Clifford resources. In a transverse-field Ising chain realizing disorder-free Stark many-body localization, we show that the stabilizer Rényi entropy remains nonzero and grows slowly to a finite plateau deep in the strong Stark-field regime, with strong initial-state selectivity. As the Stark field strength increases, long-time magic and entanglement consistently signal a crossover from ergodic to constrained localized dynamics. These results establish nonstabilizerness (``magic'') as a practical complexity probe for disorder-free ergodicity breaking and constrained localization, with direct relevance to benchmarking and designing near-term quantum simulators, and fill a gap in the understanding of nonstabilizerness in disorder-free many-body localization.