Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermal phase transitions of supersolids in the extended Bose-Hubbard
  model   We investigate numerically the finite-temperature phase diagrams of the
extended Bose-Hubbard model in a two-dimensional square lattice. In particular,
we focus on the melting of supersolid phases of two different crystal
orderings, stripe and star orders, arising from the competition of the nearest-
and next-nearest -neighbor interactions in the vicinity of quarter filling. The
two crystal orders are the result of broken translational symmetry in either
one or in both $x$, and $y$ directions. The broken gauge symmetry of the
supersolids are found to be restored via a Kosterlitz-Thouless transition while
the broken translational symmetries are restored via a single second-order
phase transition, instead of two second-order transitions in the Ising
universality class. On the other hand, the phase transitions between the star
and stripe orders are first order in nature.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom