Logarithmic growth of local entropy and total correlations in many-body localized dynamics

Fabio Anza1, Francesca Pietracaprina2, and John Goold3

1Complexity Sciences Center, Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616
2Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, France
3School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland

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Abstract

The characterizing feature of a many-body localized phase is the existence of an extensive set of quasi-local conserved quantities with an exponentially localized support. This structure endows the system with the signature logarithmic in time entanglement growth between spatial partitions. This feature differentiates the phase from Anderson localization, in a non-interacting model. Experimentally measuring the entanglement between large partitions of an interacting many-body system requires highly non-local measurements which are currently beyond the reach of experimental technology. In this work we demonstrate that the defining structure of many-body localization can be detected by the dynamics of a simple quantity from quantum information known as the total correlations which is connected to the local entropies. Central to our finding is the necessity to propagate specific initial states, drawn from the Hamiltonian unbiased basis (HUB). The dynamics of the local entropies and total correlations requires only local measurements in space and therefore is potentially experimentally accessible in a range of platforms.

Localization phenomena in interacting quantum systems have recently received a lot of attention from the scientific community, both for their theoretical interest and potential technological applications. Despite that, we still lack a direct experimental evidence of their most important feature: The logarithmic growth in time of entanglement among its components. In this work we show how this problem can be overcome: A smart choice of initial states guarantees that local measurements are sufficient to experimentally reveal this fascinating feature.

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