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

Strongly Correlated Electrons