Exploring Localization in Nuclear Spin Chains

TLDR

Characterizing out‑of‑equilibrium many‑body dynamics is essential for quantum technologies and fundamental physics, and the localized phase of interacting systems (MBL) displays a long‑time logarithmic growth in entanglement entropy that distinguishes it from noninteracting Anderson localization, though entanglement is difficult to measure experimentally. The study aims to determine whether localization quenches quantum thermalization and survives in the presence of interactions, introducing a novel correlation metric that can differentiate MBL from AL. By engineering the natural Hamiltonian to controllably introduce disorder and interactions, the authors use NMR to observe localization and employ the correlation metric to distinguish MBL from AL in high‑temperature spin systems. The metric detects localization in a natural solid‑state spin system, saturating for AL while increasing logarithmically for MBL—mirroring entanglement entropy—and confirms that NMR techniques are well suited for studying localization in spin systems.

Abstract

Characterizing out-of-equilibrium many-body dynamics is a complex but crucial task for quantum applications and the understanding of fundamental phenomena. A central question is the role of localization in quenching quantum thermalization, and whether localization survives in the presence of interactions. The localized phase of interacting systems (many-body localization, MBL) exhibits a long-time logarithmic growth in entanglement entropy that distinguishes it from the noninteracting Anderson localization (AL), but entanglement is difficult to measure experimentally. Here, we present a novel correlation metric, capable of distinguishing MBL from AL in high-temperature spin systems. We demonstrate the use of this metric to detect localization in a natural solidstate spin system using nuclear magnetic resonance (NMR). We engineer the natural Hamiltonian to controllably introduce disorder and interactions and observe the emergence of localization. In particular, while our correlation metric saturates for AL, it keeps increasing logarithmically for MBL, a behavior reminiscent of entanglement entropy, as we confirm by simulations. Our results show that our NMR techniques, akin to measuring out-of-time correlations, are well suited for studying localization in spin systems.