Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fate of the extended states in a vanishing magnetic field: the role of
  spins in strongly-interacting 2D electron systems   In non-interacting or weakly-interacting 2D electron systems, the energy of
the extended states increases as the perpendicular magnetic field approaches
zero: the extended states "float up" in energy, giving rise to an insulator.
However, in those 2D systems where metallic conductivity has been recently
observed in zero magnetic field, the energy of the extended states remains
constant or even decreases as B -> 0, thus allowing conduction in the limit of
zero temperature. Here we show that aligning the electrons' spins causes the
extended states to once more "float up" in energy in the vanishing
perpendicular magnetic field, as they do for non- or weakly-interacting
electrons. The difference between extended states that float up (an insulator)
or remain finite (a metal) is thus tied to the existence of the spins.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat