Anyon Condensation Web in 2D Modulated Gauge Theories

We introduce an anyon condensation web that interconnects a broad class of two dimensional spatially modulated gauge theories at a microscopic level. We find that condensation of anyons triggers the emergence of additional modulated symmetries, which has the general effect of increasing the number of super-selection anyon sectors, as well as the ground state degeneracy for systems with periodic boundary conditions. With this, we manage to connect several well known fracton-like states in exactly solvable ZN models as different phases of local Hamiltonians.