what is the difference between the trivial SPT phase and nontrivial SPT phase?

Question

I read some paper and found two terms "trivial SPT" and "nontrivial SPT". I am wondering what is the difference between trivial SPT and nontrivial SPT. Thank you!

SPT stands for symmetry-protected topological.

Answer 1

In general, Symmetry protected topological (SPT) phases are formed by gapped short-range entangled quantum states that do not break any symmetry (Phys. Rev. B 80, 155131 (2009)). Contrary to trivial symmetric states, a nontrivial SPT state cannot be transformed into direct product state (or Slater determinant state for fermions) of local atomic basis via symmetric local unitary transformations. Nontrivial SPT states are characterized by their gapless or degenerate edge states at open boundaries. When the symmetry is explicitly broken by perturbations, the nontrivial SPT phases can be adiabatically connected to the trivial phase and the boundary can be gapped out.