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

TL;DR

This paper investigates Bose-Hubbard models on diamond necklace lattices, revealing Hilbert space fragmentation, weak thermalization, and diverse entanglement behaviors due to localized states and conserved quantities.

Contribution

It uncovers Hilbert space fragmentation in these models, introduces a basis rotation to analyze sub-sector structure, and links this to weak thermalization and entanglement properties.

Findings

Hilbert space fragments into disconnected sub-sectors.

Entanglement entropy shows a nested-dome distribution.

Weak thermalization with varying entanglement growth observed.

Abstract

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