Fig. 1. Illustration of the experimental setup and the structure of the Hilbert space.

a Schematic of the tilted 1D Fermi-Hubbard model (with odd o and even e sites) with tunneling J, on-site interaction U and spin-dependent tilt Δ_↑, Δ_↓ (spin-up red, spin-down blue). b Dominant resonant tunneling processes for different regimes. c Finite-time connectivity ${\mathcal{C}}_{ϵ}$ (for a cut-off ϵ = 10%) defined as the fraction of states that participate in the dynamics up to an evolution time $T_{\mathcal{N}}=1000\tau$ (main text, “Methods”). The calculation was performed for a Néel-ordered singlon CDW initial state, using exact diagonalization (ED) with system size L = 13 and Δ_↑ = Δ_↓ ≡ Δ. In the large-tilt limit, Δ/J → ∞, we find emergent strongly-fragmented effective Hamiltonians for regime ① and ② (see Supplementary Note 3 and 4).