Lattice model constructions for gapless domain walls between topological phases

Domain walls between different topological phases are one of the most interesting phenomena that reveal non-trivial bulk properties phases. Very recently, gapped domain have been intensively studied. In this paper, we systematically construct a large class lattice models for gapless twisted and untwisted gauge theories with arbitrary finite group $G$. As simple examples, numerically study several groups(including both Abelian non-Abelian such as $S_3$) in $2$D using state-of-the-art loop optimization tensor network renormalization algorithm. We also propose physical mechanism understanding nature these particular wall models. Finally, by taking advantage classification construction cohomology theory, generalize constructions into dimensions, which might provide us systematical way to understand quantum phase transitions.