  Quantum many-body scar is a recently discovered phenomenon weakly violating
eigenstate thermalization hypothesis, and it has been extensively studied
across various models. However, experimental realizations are mainly based on
constrained models such as the $PXP$ model. Inspired by recent experimental
observations on the superconducting platform in Refs.~[Nat. Phys. 19, 120
(2022)] and [arXiv:2211.05803], we study a distinct class of quantum many-body
scars based on a half-filling hard-core Bose-Hubbard model, which is generic to
describe in many experimental platforms. It is the so-called Hilbert space
quantum scar as it originates from a subspace with a hypercube geometry weakly
connecting to other thermalization regions in Hilbert space. Within the
hypercube, a pair of collective Fock states do not directly connect to the
thermalization region, resulting in slow thermalization dynamics with
remarkable fidelity revivals with distinct differences from dynamics of other
initial states. This mechanism is generic in various real-space lattice
configurations, including one-dimensional Su-Schrieffer-Heeger chain, comb
lattice, and even random dimer clusters consisting of dimers. In addition, we
develop a toy model based on Hilbert hypercube decay approximation, to explain
the spectrum overlap between the collective states and all eigenstates.
Furthermore, we explore the Hilbert space quantum scar in two- and
three-dimensional Su-Schrieffer-Heeger many-body systems, consisting of
tetramers or octamers, respectively. This study makes quantum many-body scar
state more realistic in applications such as quantum sensing and quantum
metrology.
