Two-dimensional symmetry-protected topological phases with PSU(N) and time-reversal symmetry

Symmetry-protected topological phase is one type of nontrivial quantum disordered many-body state of matter. In this paper we study one class of symmetry-protected topological phases in two-dimensional space with both PSU(N) and time-reversal symmetry. These states can be described by a principal chiral model with a topological Θ term. As long as the time-reversal symmetry and PSU(N) symmetry are both preserved, the (1+1)-dimensional boundary of this system must be either gapless or degenerate. We will also construct a wave function of a spin-1 system on the honeycomb lattice, which is a candidate for the symmetry-protected topological phase with both SO(3) and time-reversal symmetry.