Hilbert Space Fragmentation in Hardcore Bose and Fermi Hubbard Models on Generalized Lieb Lattices

TL;DR

This paper investigates Hilbert space fragmentation in hardcore Bose and Fermi Hubbard models on generalized Lieb lattices, revealing exact eigenstates, weak fragmentations, and connections to quantum scars.

Contribution

It introduces a family of models with RSGA structure, demonstrating quantum HSF and exact condensate eigenstates, and explores the relation to quantum scars in fermionic models.

Findings

Existence of quantum Hilbert space fragmentation in the models.

Construction of exact condensate eigenstates with off-diagonal long-range order.

Identification of energy towers and quantum scars related to {\

Abstract

We study the Hilbert space fragmentation (HSF) in hardcore Bose and Fermi Hubbard models in the framework of the restricted spectrum generating algebra (RSGA). We present a family of hardcore Bose-Hubbard models with repulsive density-density interactions on a generalized Lieb lattice. We show that this system possesses the RSGA structure in the large interaction strength limit, exhibiting quantum HSF. It allows us to construct a set of exact condensate eigenstates, possessing off diagonal long-range order. Based on numerical simulations conducted on several representative lattices, we demonstrate the existence of weak fragmentations when the constraints are not exact. As applications, we also studied the connection between HSF and RSGA in modified fermionic Hubbard models, where the {\eta}-pairing states are shown to be energy towers, acting as quantum scars.