: Emanant and Emergent Symmetry Topological Order from Low-Energy Spectrum

by Oemer Aksoy

Tuesday 26 May 2026, 11:00 → 12:00 Europe/Zurich

Teams

Given a microscopic quantum model, new symmetries may arise in its low-energy and long-wavelength limit. These emergent and/or emanant symmetries may differ substantially from those of the underlying microscopic model as they may be anomalous, higher-form, higher-group or non-invertible. A systematic way to describe the universal properties of systems with such (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. 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 (CFT) at the self-dual radius. I will show how one can identify the appropriate symTO that correctly captures the gapped phases neighboring this critical point and their symmetry breaking patterns. I will conclude by discussing how the symTO description carries the signatures of the emergent SO(4) symmetry in the compact boson CFT, along with some conjectures.