Local Hilbert space fragmentation and weak thermalization in Bose-Hubbard diamond necklaces

We study Bose-Hubbard models in a family of diamond necklace lattices with $n$ central sites. The single-particle spectrum these presents compact localized states (CLSs) that occupy the up and down sites each diamond. By performing an appropriate basis rotation, fragmentation many-boson Hilbert space becomes apparent adjacency graph Hamiltonian, showing disconnected sub-sectors wide range dimensions. present conserved quantity related to occupation CLSs uniquely identifies different space. Due space, distribution entanglement entropies system nested-dome structure. find weak thermalization through sub-sector-restricted evolution entropy scalings from area-law logarithmic growth. Additionally, we observe how distinguishability between domes increases number explain mechanism behind this fact by analyzing structure Hamiltonian.