Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multifractal Scalings across the Many-Body Localization Transition   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 ${\cal{N}}\simeq 2.7\,10^6$). 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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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con