Subsystem symmetry protected topological order

TL;DR

This paper introduces a new class of topological phases protected by subsystem symmetries acting on lower-dimensional subsets, with exactly solvable models demonstrating their unique properties and relation to fracton phases.

Contribution

It constructs exactly solvable 2D and 3D models of subsystem symmetry protected topological phases with novel symmetry and topological features.

Findings

Existence of gapless edge modes in SSPT phases

Realization of projective symmetry actions at edges

Identification of non-local order parameters for SSPT phases

Abstract

In this work, we introduce a new type of topological order which is protected by subsystem symmetries which act on lower dimensional subsets of lattice many-body system, e.g. along lines or planes in a three dimensional system. The symmetry groups for such systems exhibit a macroscopic number of generators in the infinite volume limit. We construct a set of exactly solvable models in $2d$ and $3d$ which exhibit such subsystem SPT (SSPT) phases with one dimensional subsystem symmetries. These phases exhibit analogs of phenomena seen in SPTs protected by global symmetries: gapless edge modes, projective realizations of the symmetries at the edge and non-local order parameters. Such SSPT phases are proximate, in theory space, to previously studied phases that break the subsystem symmetries and phases with fracton order which result upon gauging them.