Leinweber Seminar: Emanant and emergent symmetry-topological-order from low-energy spectrum. - Omer Mert Aksoy, MIT

In a given model, its low-energy emergent and/or emanant symmetries can be anomalous, higher-group, or non-invertible. A systematic way to describe the universal properties of systems with generalized symmetries is through a topological field theory in one higher dimension, also known as the symmetry topological order (symTO). In this talk, I will describe a method to compute the (emanant/emergent) symTO of a 1+1D system from its low-energy spectra under closed boundary conditions with all possible symmetry twists. In particular, I will apply this method to the antiferromagnetic spin-1/2 Heisenberg chain, whose low-energy properties are described by the compact boson conformal field theory at self-dual radius. I will then identify the corresponding emanant symTO as the D8 quantum double, when we restrict ourselves to the Z2xZ2 subgroup of the SO(3) spin-rotation symmetry and lattice translations. I will finally show how this emanant symTO carries signatures of the emergent SO(4) symmetry and discuss the possible neighboring phases using its condensable algebras.