Self-correction from higher-form symmetry protection on a boundary

TL;DR

This paper demonstrates how to replace explicit bulk 1-form symmetry with an emergent one, reducing complexity and linking boundary defects to bulk topological order, advancing understanding of self-correcting quantum memories.

Contribution

It introduces a method to replace explicit bulk 1-form symmetry with an emergent symmetry, simplifying the enforcement to boundary terms and connecting boundary defects to bulk topological order.

Findings

Emergent 1-form symmetry reduces bulk enforcement complexity.

Boundary symmetry enforcement scales as O(L^2) instead of O(L^3).

Boundary defects exhibit interesting memory properties without symmetry.

Abstract

Recent work has shown that a self-correcting memory can exist in 3 spatial dimensions, provided it is protected by a 1-form symmetry. Requiring that a system's dynamics obey this type of symmetry is equivalent to enforcing a macroscopic number of symmetry terms throughout the bulk. In this paper, we show how to replace the explicit 1-form symmetry in the bulk with an emergent 1-form symmetry. Although the symmetry still has to be explicitly enforced on the boundary, this only requires O(L^2) terms instead of O(L^3) terms. We then reinterpret this boundary as a symmetry-protected topological defect in a bulk topological order. Defects can have interesting memory properties even in the absence of symmetry.