Probing Hilbert Space Fragmentation with Strongly Interacting Rydberg Atoms

TL;DR

This paper explores Hilbert space fragmentation in a Rydberg atom system, demonstrating tunable ergodicity, localization phenomena, and the effects of nonlocal interactions and disorder, with implications for quantum simulation.

Contribution

It proposes a feasible scheme to study Hilbert space fragmentation on Rydberg simulators, revealing tunable ergodicity and localization phenomena through a mapped generalized folded XXZ model.

Findings

Hilbert space fragmentation can be realized in Rydberg systems.

Tuning of ergodicity from integrable to localized phases.

Disorder induces symmetry-selective many-body localization.

Abstract

Hilbert space fragmentation provides a mechanism to break ergodicity in closed many-body systems. Here, we propose a feasible scheme to 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.