  In this paper, we construct an exactly solvable lattice Hamiltonian model to
investigate the properties of a composite system consisting of multiple
topological orders separated by gapped domain walls. There are interdomain
elementary excitations labeled by a pair of anyons in different domains of this
system; This system also has elementary excitations with quasiparticles in the
gapped domain wall. Each set of elementary excitations corresponds to a basis
of the ground states of this composite system on the torus, reflecting that the
ground-state degeneracy matches the number of either set of elementary
excitations. The characteristic properties of this composite system lie in the
basis transformations, represented by the $S$ and $T$ matrices: The $S$ matrix
encodes the mutual statistics between interdomain excitations and domain-wall
quasiparticles, and the $T$ matrix encapsulates the topological spins of
interdomain excitations. Our model realizes a spatial counterpart of a temporal
phase transition triggered by anyon condensation, bringing the abstract theory
of anyon condensation into manifestable spatial interdomain excitation states.
