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

TL;DR

This paper investigates how quantum magic, a resource for quantum computation, develops slowly and saturates in a disorder-free many-body localized system, providing insights into ergodicity breaking and quantum complexity.

Contribution

It demonstrates that stabilizer Rényi entropy reveals slow growth and saturation of quantum magic in Stark many-body localization, serving as a practical diagnostic for constrained quantum dynamics.

Findings

Quantum magic remains finite and grows slowly before saturating.

Increasing Stark gradient causes a crossover from ergodic to localized behavior.

Stabilizer magic can diagnose ergodicity breaking in disorder-free systems.

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.