1+1d SPT phases with fusion category symmetry: interface modes and non-abelian Thouless pump

Shuhei Ohyama (Vienna University)

Fusion category symmetry is the most general finite symmetry in 1+1 dimensional systems. We investigated gapped phases defined on a lattice with fusion category symmetry using the technique of matrix product states, focusing on the following aspects:

1. SPT invariants
2. Bulk-boundary correspondence/Thouless pump
3. Classification of a parametrized family of general gapped phases

In my talk, I would like to explain these topics, particularly topics 1 and 2. This talk is mainly based on joint work arXiv:2408.15960 with Kansei Inamura.