In this talk, I will present a new systematic approach of constructing solvable lattice Hamiltonians for a large class of 2+1D topological orders, which are enriched by background Electromagnetic U(1) symmetry and feature non-trivial fractional Hall conductivity. This approach goes beyond the conventional fixed-point principle by considering small, non-commuting terms adding to the commuting projectors, thus circumventing the limitation of Kapustin-Fidkowski no-go theorem. The detailed procedure, including a generalized “Villain-ization” method for 1-form symmetries, will be discussed in detail.
References: Phys. Rev. B 105, 155130 (2022); J. High Energ. Phys. 2023, 130 (2023)