Lattice model constructions for gapless domain walls of topological phases

Shuo Yang

Lattice models of gapless domain walls between twisted and untwisted quantum double models are constructed systematically. As a simple example, we numerically study the gapless domain walls between toric code model and double semion model using the state-of-art Loop tensor network renormalization (Loop-TNR) algorithm. Surprisingly, we find a conformal field theory described by the orbifold double su(2)_1 Wess-Zumino-Witten model even in the absence of global SU(2) symmetry for such a gapless domain wall. By taking advantage of the systematic classification and construction of twisted quantum double models and their corresponding SPT phases using group cohomology theory, we formally constructed general lattice models of these domain wall models for arbitrary finite symmetry group. Finally, we generalize the constructions in arbitrary dimensions and discuss potential physical interpretations for gapless domain walls in higher dimensions.

http://scgp.stonybrook.edu/video_portal/video.php?id=3489

Simons- Workshop: Tensor-Network Methods: Structure, Applications and Holography