Higgs Condensates are Symmetry-Protected Topological Phases: I. Discrete Symmetries

Understand

Where in the landscape of many-body phases of matter do we place the Higgs condensate of a gauge theory? On the one hand, the Higgs phase is gapped, has no local order parameter, and for fundamental Higgs fields is adiabatically connected to the confined phase.

• On the other hand, Higgs phases such as superconductors display rich phenomenology.
• In this work, we propose a minimal description of the Higgs phase as a symmetry-protected topological (SPT) phase, utilizing conventional and higher-form symmetries.
• In this first part, we focus on 2+1D $\mathbb Z_2$ gauge theory and find that the Higgs phase is protected by a higher-form magnetic symmetry and a matter symmetry, whose meaning depends on the physical context.