Exact emergent higher-form symmetries in bosonic lattice models

Understand

Although condensed matter systems usually do not have higher-form symmetries, we show that, unlike 0-form symmetry, higher-form symmetries can emerge as exact symmetries at low energies and long distances.

• In particular, emergent higher-form symmetries at zero temperature are robust to arbitrary local UV perturbations in the thermodynamic limit.
• This result is true for both invertible and non-invertible higher-form symmetries.
• Therefore, emergent higher-form symmetries are $\textit{exact emergent symmetries}$: they are not UV symmetries but constrain low-energy dynamics as if they were.