Ultraslow Growth of Number Entropy in an l-bit Model of Many-Body Localization

TL;DR

This paper shows that in an l-bit model of many-body localization, the number entropy grows extremely slowly over time, indicating that such slow growth alone does not disprove localization.

Contribution

The authors construct a random circuit l-bit model with localized bits and decaying interactions, demonstrating ultraslow number entropy growth consistent with many-body localization.

Findings

Number entropy exhibits ultraslow growth after a quench from a local product state.

The saturation value of number entropy increases with system size.

Slow growth of number entropy alone cannot rule out 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 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 N\'eel 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.