  Gutzwiller projection is a way to construct many-body wave functions that
could carry topological order or symmetry protected topological (SPT) order.
However, an important issue is to determine whether or not a given
Gutzwiller-projected wave functions (GWF) carries a non-trivial SPT order, and
which SPT order is carried by the wavefunction. In this paper, we numerically
study the SPT order in a spin $S = 1$ GWF on the Kagome lattice. Using the
standard Monte Carlo method, we directly confirm that the GWF has (1) gapped
bulk with short-range correlations, (2) a trivial topological order via
nondegenerate ground state, and zero topological entanglement entropy, (3) a
non-trivial $U(1)\times U(1)$ SPT order via the Hall conductances of the
protecting $U(1)\times U(1)$ symmetry, and (4) symmetry protected gapless
boundary. This represents numerical evidence of continuous symmetry protected
topological order in two-dimensional bosonic lattice systems.

Strongly Correlated Electrons;Quantum Physics