Spontaneous loop-spin current with topological characters in the Hubbard model

We find a state characterized by a spontaneous loop-spin current and a single-particle gap in the Hubbard model within the variational cluster approach. This state exists for arbitrarily small interaction in a half-filled honeycomb lattice. Moreover, from the calculations of the topological invariants for the interacting system, it is shown that this gapped state has nontrivial topological characters; this state is the topological Mott insulating state. This result implies the ubiquity of topological Mott insulating phases.