Duality on the lattice and application to gapped/gapless topological phases

Topological phases of matter are classified based on the global symmetries of physical systems. When a system has a global symmetry, we can define duality transformations, such as gauging and fermionization. These transformations are also defined for lattice models. The dual model exhibits a dual global symmetry, while the original symmetry becomes local after the duality transformation. In this talk, we introduce the way to construct lattice models for various types of topological phases using dualities. Our models exhibit the same behavior as the usual dual model in the infrared (IR) regime. To achieve this, we enforce the Gauss law constraint as an energy cost. We point out that the model is generally different from the usual dual model in terms of topological phases. This difference arises from the requirement to treat an original global symmetry, which becomes local in the IR, as a global symmetry in our construction. As an application, we discuss a systematic approach for constructing models representing gapless topological phases.