Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: State diagram and the phase transition of $p$-bosons in a square
  bi-partite optical lattice   It is shown that, in a reasonable approximation, the quantum state of
$p$-bosons in a bi-partite square two-dimensional optical lattice is governed
by the nonlinear boson model describing tunneling of \textit{boson pairs}
between two orthogonal degenerate quasi momenta on the edge of the first
Brillouin zone. The interplay between the lattice anisotropy and the atomic
interactions leads to the second-order phase transition between the
number-squeezed and coherent phase states of the $p$-bosons. In the isotropic
case of the recent experiment, Nature Physicis 7, 147 (2011), the $p$-bosons
are in the coherent phase state, where the relative global phase between the
two quasi momenta is defined only up to mod($\pi$): $\phi=\pm\pi/2$. The
quantum phase diagram of the nonlinear boson model is given.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga