Intrinsically average symmetry-protected topological phases

Symmetry-protected topological (SPT) phases are topologically nontrivial gapped phases of quantum many-body systems protected by certain global symmetry. The notion of SPT order has been recently generalized to systems where the symmetry is broken by quenched disorder, but preserved on average by the disorder ensemble, In this work we present a systematic classification of such SPT phases using a decorated domain wall approach. In particular, we show that there are average SPT phases which do not exist in clean systems, thus are intrinsically disordered. We will present examples of intrinsically average SPT phases and discuss their boundary states.