Bulk Excitations of Invertible Phases

TL;DR

This paper explores bulk excitations in invertible phases like SPT and topological superconductors, revealing a one-to-one correspondence with excitations in trivial product states through topological holography and boundary analysis.

Contribution

It establishes a universal correspondence between bulk excitations in invertible phases and those in trivial states, extending understanding of topological phases and boundary conditions.

Findings

Bulk excitations in invertible phases correspond to those in trivial states.

Symmetric Quantum Cellular Automaton maps SPT states to product states.

Boundary conditions of topological states have only relative distinctions.

Abstract

Recent developments in the study of topological defects highlight the importance of understanding the multi-dimensional structure of bulk excitations inside a quantum system. When the bulk ground state is trivial, i.e. a product state, excitations on top of it are decoupled from each other and correspond to lower-dimensional phases and their defects within. In this paper, we expand the discussion to invertible phases and study the bulk excitations in, for example, SPT phases, Majorana chains, p + ip superconductors etc. We find that there is a one-to-one correspondence between bulk excitations inside a nontrivial invertible phase and those in a product state. For SPT phases, this can be shown using the symmetric Quantum Cellular Automaton that maps from the product state to the SPT state. More generally, for invertible phases realizable using the Topological Holography construction, we demonstrate the correspondence using the fact that certain gapped boundary conditions of a topological bulk state have only relative distinctions but no absolute ones.