Quasi-Topological Phases of Matter and Topological Protection

TL;DR

This paper introduces the concept of quasi-topological phases, which exhibit some topological properties without being fully topological, and discusses their implications for information protection, especially in Majorana systems.

Contribution

It formulates the notion of quasi-topological and symmetry-protected quasi-topological phases, providing a framework to understand systems that are partially topological.

Findings

Quasi-topological phases are distinct from true topological phases.

Examples include Ising-type (Majorana) systems relevant to current research.

Quasi-topological phases offer greater stability than previously recognized.

Abstract

We discuss systems which have some, but not all of the hallmarks of topological phases. These systems' topological character is not fully captured by a local order parameter, but they are also not fully described at low energies by topological quantum field theories. For such systems, we formulate the concepts of quasi-topological phases (to be contrasted with true topological phases), and symmetry-protected quasi-topological phases. We describe examples of systems in each class and discuss the implications for topological protection of information and operations. We explain why topological phases and quasi-topological phases have greater stability than is sometimes appreciated. In the examples that we discuss, we focus on Ising-type (a.k.a. Majorana) systems particularly relevant to recent theoretical advances and experimental efforts.