  Hilbert space fragmentation provides a mechanism to break ergodicity in
closed many-body systems. Here, we propose a realistic scheme to
comprehensively explore this exotic paradigm on a Rydberg quantum simulator. We
show that the Rydberg Ising model in the large detuning regime can be mapped to
a generalized folded XXZ model featuring a strongly fragmented Hilbert space.
The emergent Hamiltonian, however, displays distinct time scales for the
transport of a magnon and a hole excitation. This interesting property
facilitates a continuous tuning of the Krylov-subspace ergodicity, from the
integrable regime, to the Krylov-restricted thermal phase, and eventually to
the statistical bubble localization region. By further introducing nonlocal
interactions, we find that both the fragmentation behavior and the ergodicity
of the Krylov subspace can be significantly enriched. We also examine the role
of atomic position disorders and identify a symmetry-selective many-body
localization transition. We demonstrate that these phenomena manifest
themselves in quench dynamics, which can be readily probed in state-of-the-art
Rydberg array setups.
