  Bosonic symmetry protected topological (BSPT) states, the bosonic analogue of
topological insulators, have attracted enormous theoretical interest in the
last few years. Although BSPT states have been classified by various
approaches, there is so far no successful experimental realization of any BSPT
state in two or higher dimensions. In this paper, we propose that a two
dimensional BSPT state with $U(1) \times U(1)$ symmetry can be realized in
bilayer graphene in a magnetic field. Here the two $U(1)$ symmetries represent
total spin $S^z$ and total charge conservation respectively. The Coulomb
interaction plays a central role in this proposal -- it gaps out all the
fermions at the boundary, so that only bosonic charge and spin degrees of
freedom are gapless and protected at the edge. Based on the bosonic nature of
the boundary states, we derive the bulk wave function for the bosonic charge
and spin degrees of freedom, which takes exactly the same form as the desired
BSPT state. We also propose that the bulk quantum phase transition between the
BSPT and trivial phase, could become a "bosonic phase transition" with
interactions. That is, only bosonic modes close their gap at the transition,
which is fundamentally different from all the well-known topological insulator
to trivial insulator transitions which occur for free fermion systems. We
discuss various experimental consequences of this proposal.

Strongly Correlated Electrons