Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries

Understand

In this work, we analyze the macroscopic observables in the 1+1D gapped phases with Abelian onsite symmetries and show that the spacetime observables for each gapped phase form a clear structure that can be mathematically described by enriched fusion categories, which uncovers the behavior of nonlocal excitations that were blurry in traditional Landau paradigm.

• These categorical descriptions not only generate the known classification results for symmetry preserving and breaking phases, but also unifies lattice dualities in a broader picture.
• After analyzing the general lattice model together with their boundaries, we give explicit examples including nontrivial SPT phase, where nontrivial boundaries can be given directly through our classification.
• Using enriched categorical descriptions, the lattice dualities and their gapped phases are unified under a holographic duality between an 2d.