Information-theoretic perspective of emergent 1-form symmetries and symmetry-protected phases of matter

Abstract: Higher-from symmetries act on sub-dimensional spatial manifolds of a quantum system and they can emerge as an exact symmetry at low energies even when they are explicitly broken at the microscopic level. In this talk, we present an information-theoretic perspective on the emergence of higher-form symmetries, viewing their emergence in terms of how information associated with a microscopic symmetry is preserved under perturbations. This allows the emergence of a low-energy effective symmetry operator independent of the microscopic details of the perturbation, unlike the one directly obtained from quasi-adiabatic continuation. We illustrate this framework using perturbed toric-code models. We then apply it to symmetry-protected topological phases protected by 1-form symmetries, showing how it provides a natural understanding of "emergent 1-form SPT phases", as well as the emergence of symmetries at different energy scales.