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

Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model