Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Order-by-Disorder Degeneracy Lifting of Interacting Bosons on the Dice
  Lattice   Motivated by recent experimental progress in the realization of synthetic
gauge fields in systems of ultracold atoms, we consider interacting bosons on
the dice lattice with half flux per plaquette. All bands of the non-interacting
spectrum of this system were previously found to have the remarkable property
of being completely dispersionless. We show that degeneracies remain when
interactions are treated at the level of mean field theory, and the ground
state exhibits vortex lattice configurations already established in the simpler
XY model in the same geometry. We argue that including quantum and thermal
fluctuations will select a unique vortex lattice up to overall symmetries based
on the order-by-disorder mechanism. We verify the stability of the selected
state by analyzing the condensate depletion. The latter is shown to exhibit an
unusual non-monotonic behavior as a function of the interaction parameters
which can be understood as a consequence of the dispersionless nature of the
non-interacting spectrum. Finally, we comment on the role of domain walls which
have interactions mediated through fluctuations.

2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph