Physics and Astronomy Calendar

We show that the surface states of three-dimensional bosonic symmetry protected topological (SPT) phases with unitary symmetries are protected: their surface must be gapless as long as the symmetry is not broken and the surface is not topologically ordered. We demonstrate the result by constructing an exactly soluble lattice model which realizes a nontrivial Z₂×Z₂ SPT phase in three dimensions and showing that the model has protected surface states.