Trapping hard-core bosons in flat-band lattices

We investigate one-dimensional (1D) and 2D cross-stitch lattices with hard-core bosons and analytically construct exact ground states that feature macroscopic degeneracy. The construction relies on the presence of a flat band in the single particle spectrum and the orthogonality of the associated compact localized states (CLS). Up to filling fraction ν=1/2, the ground state is constructed by occupying the CLS. Exactly at ν=1/2, the ground state becomes a Wigner crystal. For higher filling fractions, the ground state is constructed by filling the CLS sites completely one by one. Macroscopic degeneracy arises from the multiple choices available when occupying or filling the CLS sites. An occupied CLS acts as an impenetrable barrier for bosons both in 1D and 2D, leading to Hilbert space fragmentation. A similar phenomenology also holds for hard-core bosons on the diamond chain and its higher dimensional generalizations. We also discuss the mapping of these hard-core models onto spin models with quantum many-body scars.