Ultraslow Growth of Number Entropy in an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>ℓ</mml:mo> </mml:math> -Bit Model of Many-Body Localization

Abstract

We demonstrate that slow growth of the number entropy following a quench from a local product state is consistent with many-body localization. To do this, we construct a novel random circuit ℓ-bit model with exponentially localized ℓ-bits and exponentially decaying interactions between them. We observe an ultraslow growth of the number entropy starting from a Néel state, saturating at a value that grows with system size. This suggests that the observation of such growth in microscopic models is not sufficient to rule out many-body localization.

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