Universality of duality-to-symmetry-broken-phase mapping

Determine whether every phase of one-dimensional quantum lattice models with (possibly categorical) symmetries admits a duality mapping that takes it to a completely symmetry-broken phase with respect to the dual symmetry, generalizing examples such as Kramers–Wannier and Kennedy–Tasaki dualities.

Background

The notes analyze dualities implemented by matrix product operator intertwiners and show, in concrete examples like Kramers–Wannier and Kennedy–Tasaki, that phases can be mapped to symmetry-broken counterparts under a suitable duality.

They conjecture that this observation may hold universally across phases in one-dimensional models with generalized symmetries, which would have significant implications for phase classification and numerical simulation strategies.