Obstructions to SPT-Like Physics in QBHs

We apply the results of the previous two chapters to study certain topological aspects of QBHs. First, we leverage the duality of Chap. 4 to establish a connection between bosonic Berry phases and the more standard Berry phases encountered, for instance, in topological non-interacting fermionic systems. Following this, we recap the essential features of SPT phases in non-interacting fermions by means of a simple analysis of the fermionic Kitaev chain. We proceed to describe the practical and theoretical challenges towards realizing these features in QBHs. First, we describe the no-go theorems forbidding SPT phases in thermodynamically stable QBHs. Then, by forgoing the thermodynamic stability assumption, we explore the intrinsic instability of any zero energy edge modes that may arise. We illustrate these points by uncovering explicit bosonic “shadows” of Majorana fermions in a dynamically, and thermodynamically, unstable generalization of the BKC.