Higher-form entanglement asymmetry and topological order
Phys. Rev. B 114, 105119 – Published 14 August, 2026
DOI: https://doi.org/10.1103/hb3m-kg89
Abstract
We extend a recently defined measure of symmetry breaking, the entanglement asymmetry, to higher-form symmetries. In particular, we focus on Abelian topological order in two dimensions, which spontaneously breaks a 1-form symmetry. Using the toric code as a primary example, we compute the entanglement asymmetry and compare it to the topological entanglement entropy. We find that while the two quantities are not strictly equivalent, both are subleading corrections to the area law and can serve as order parameters for the topological phase. We generalize our results to Abelian topological order and express the maximal entanglement asymmetry in terms of the number of anyon species. Finally, we discuss how the scaling of entanglement asymmetry correctly detects topological order in the deformed toric code, where 1-form symmetry breaking persists even in a nontopological phase.
