Many-body localization and ergodicity in disordered long-range Ising models
Although a quantum version of the classical ergodic theorem has been put forward already by von Neumann in 1929, a general understanding of quantum ergodicity has not yet been achieved. Recently, it has been proposed that a general framework for quantum ergodicity could be given by the concept of many-body localization. Since in a many-body localized phase all eigenfunctions are localized, such phases may be inherently robust against local errors and could be useful in the context of quantum memory devices. However, compared to single-particle localization, many-body localization suffers from an increased complexity, making it challenging to derive the localization properties of a given system and finding suitable, experimentally accessible quantities for their characterization.
In this talk, we present recent analytical and numerical results for a quantum many-body system that can be realized in state-of-the-art trapped-ion experiments, a long-range Ising models with disorder in the transverse-field. As we show, this model enters a many-body localized phase at any non-vanishing disorder strength. We discuss how this model can be implemented in current experiments, and we identify a general measure for quantum ergodicity that can be obtained through experimentally accessible, single-particle observables.
Host: Chris Monroe
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