Trapping Hard-Core Bosons in Flatband Lattices
arxiv(2024)
摘要
We investigate 1D and 2D cross-stitch lattices with hard-core bosons and
analytically construct exact groundstates that feature macroscopic degeneracy.
The construction relies on the presence of a flatband in the single particle
spectrum and the orthogonality of the associated compact localized states
(CLS). Up to filling fraction ν=1/2, the groundstate is constructed by
occupying the CLS. Exactly at ν=1/2, the groundstate becomes a Wigner
crystal. For higher filling fractions, the groundstate 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.
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