| Summary: | We show that finite lattices with arbitrary boundaries may support large degenerate subspaces, stemming from the underlying translational symmetry of the lattice. When the lattice is coupled to an environment, a potentially large number of these states remains weakly or perfectly uncoupled from the environment, realizing a new kind of bound states in the continuum. These states are strongly localized along particular directions of the lattice, which, in the limit of strong coupling to the environment, leads to spatially localized subradiant states.
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