Exploring Localization in Nuclear Spin Chains

Abstract

Characterizing out-of-equilibrium many-body dynamics is a complex but crucial task for quantum applications and understanding fundamental phenomena. A central question is the role of localization in quenching thermalization in many-body systems and whether such localization survives in the presence of interactions. Probing this question in real systems necessitates the development of an experimentally measurable metric that can distinguish between different types of localization. While it is known that 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 case of Anderson localization (AL), entanglement entropy 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 solid-state 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 slowly keeps increasing for MBL, demonstrating analogous features to entanglement entropy, as we show in simulations. Our results show that our NMR techniques, akin to measuring out-of-time correlations, are well suited for studying localization in spin systems.

Loschmidt echo in many-body localized phases

“…27 However, most of the evidence for the MBL phase consists of the absence of complete relaxation in the presence of interactions, and characteristic signatures of the MBL dynamics were not yet observed (see however recent experiments 27,28 ). While measuring entanglement spreading experimentally is generally a very hard problem, the same dephasing dynamics could be detected in the relaxation of observables in a global quench, 24 modified spin-echo type setups, 25 quantum revivals, 29 and other dynamical experimental signatures of the MBL phase.…”

Onset of many-body chaos in the O(N) model

“…At the other extreme, disordered quantum systems typically scramble much more slowly than their clean counterparts [27][28][29][30][31][32]. Several experimental proposals have also appeared recently [33][34][35] that enable one to measure OTO correlators and scrambling and three preliminary experiments have already been carried out [36][37][38]. There has been a flurry of recent calculations of out-of-time order correlators in a variety of models [39][40][41][42][43][44][45][46][47][48][49][50][51].…”

Resilience of scrambling measurements

“…The OTOC-measurement protocols that do not require time reversal suffer from other limitations that likely preclude the study of large systems. Nevertheless, progress in the control of atoms, molecules, ions, and photons has brought experimental measurements of OTOCs and scrambling seemingly within reach [29][30][31][32].…”