Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Many-Body Localization: Stability and Instability   Rare regions with weak disorder (Griffiths regions) have the potential to
spoil localization. We describe a non-perturbative construction of local
integrals of motion (LIOMs) for a weakly interacting spin chain in one
dimension, under a physically reasonable assumption on the statistics of
eigenvalues. We discuss ideas about the situation in higher dimensions, where
one can no longer ensure that interactions involving the Griffiths regions are
much smaller than the typical energy-level spacing for such regions. We argue
that ergodicity is restored in dimension d > 1, although equilibration should
be extremely slow, similar to the dynamics of glasses.

6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
3
The categories of this paper are: physics
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an