Holographic Symmetries and Generalized Order Parameters for Topological Matter

TL;DR

This paper presents a universal method based on bond-algebraic dualities to identify generalized order parameters in various topological systems, highlighting the concept of holographic symmetry that relates bulk and boundary properties.

Contribution

It introduces the notion of holographic symmetry and applies a duality-based approach to find order parameters in topological and gauge theories.

Findings

Derived generalized order parameters for Abelian gauge theories

Linked holographic symmetries to edge modes and localization

Demonstrated the method's applicability to topological matter models

Abstract

We introduce a universally applicable method, based on the bond-algebraic theory of dualities, to search for generalized order parameters in disparate systems including non-Landau systems with topological order. A key notion that we advance is that of {\em holographic symmetry}. It reflects situations wherein global symmetries become, under a duality mapping, symmetries that act solely on the system's boundary. Holographic symmetries are naturally related to edge modes and localization. The utility of our approach is illustrated by systematically deriving generalized order parameters for pure and matter-coupled Abelian gauge theories, and for some models of topological matter.