Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Phase Transition: direct measurement of a mathematical
  abstraction   By viewing entanglement as a state function, a new kind of phase transition
takes place: the geometric phase transition. This phenomenon occurs due to
singularities in the shape of the entangled states set. It is shown how this
result can be carried to provide a better understanding of the geometry of
entanglement. Surprisingly, this study can be done experimentally, what allows
to determine the shape of different entangled states sets, a purely
mathematical definition, in real experiments.

11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol