  Topological phases and materials have attracted much attention in recent
years. Though many progress has been made, the effect of nonlinearity on such
system remains untouched. In this paper, by considering the mean-field
approximation in a coupled boson-hexagonal lattice system, we obtain a
different type of Dirac cone. Due to its special structure of the cone, the
Berry phase (two-dimensional Zak phase) of this new Dirac cone is quantized
differently, i.e., it has been modified due to the interactions and the
critical line between different topological phases has moved, depending on the
type of interactions. Furthermore, the new Berry phase is found to be
quantized, offering a possible nonlinear topological invariant which can supply
as a criterion of topological classification for that interacting system. The
quantum phase transition in terms of this criterion in the system has also been
examined.
