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Quantum Simulation

Multifractal Scalings across the Many-Body Localization Transition

arXiv
Authors: Nicolas Macé, Fabien Alet, Nicolas Laflorencie

Year

2018

Paper ID

39383

Status

Preprint

Abstract Read

~2 min

Abstract Words

111

Citations

N/A

Abstract

In contrast with Anderson localization where a genuine localization is observed in real space, the many-body localization (MBL) problem is much less understood in the Hilbert space, support of the eigenstates. In this work, using exact diagonalization techniques we address the ergodicity properties in the underlying {cal{N}}-dimensional complex networks spanned by various computational bases for up to L=24 spin-1/2 particles i.e. Hilbert space of size ${cal{N}}simeq 2.7 106$. We report fully ergodic eigenstates in the delocalized phase (irrespective of the computational basis), while the MBL regime features a generically (basis-dependent) multifractal behavior, delocalized but non-ergodic. The MBL transition is signaled by a non-universal jump of the multifractal dimensions.

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  • In contrast with Anderson localization where a genuine localization is observed in real space, the many-body localization (MBL) problem is much less understood in the Hilbert...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1812.10283 [2] arXiv https://arxiv.org/abs/1812.10283 [3] Publisher https://arxiv.org/abs/1812.10283

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