We report experimental evidence for disorder-free Many-Body Localization (MBL) in a fractal Heisenberg spin chain H = -J Σ α^{-n} (XX+YY+ZZ) executed on IBM Quantum hardware (ibm_kingston, 156 qubits). By replacing random disorder with a deterministic fractal coupling sequence J_n = α^{-n} at the critical parameter α ≈ 2.0 (Haldane point), we observe localization, spectral gap, sub-volume entanglement entropy, and holographic area law simultaneously without any random disorder. Twenty-two independent experiments were executed with 8,000 shots each. Key results: fractal magnetization rises 38.5%→46.2% while uniform falls 35.9%→26.2%; Floquet revival 59.71% hardware vs 59.75% simulation (0.04% error); Lieb-Robinson velocity 6× slower; Riemann curvature 2.85×; MBL transition Δ=0.739 matching Science 2015. Four theorems derived: localization bound, spectral gap ≥ 8J/3, Lieb-Robinson bound v_LR ≤ 5.44J, emergent curved spacetime metric. All IBM Quantum job IDs publicly verifiable. First experimental demonstration of geometric MBL on superconducting quantum hardware.
Disordered quantum systems undergoing a many-body localization (MBL) transition fail to reach thermal equilibrium under their own dynamics. Distinguishing between asymptotically localized or delocalized dynamics based on numerical results is, however, nontrivial due to finite-size effects. Numerical linked cluster expansions (NLCE) provide a means to tackle quantum systems directly in the thermodynamic limit but are challenging for models without translational invariance. Here we demonstrate that NLCE provides a powerful tool to explore MBL by simulating quench dynamics in disordered spin-
1/2 two-leg ladders and Fermi-Hubbard chains. Combining NLCE with an efficient real-time evolution of pure states, we obtain converged results for the decay of the imbalance on long time scales and show that, especially for intermediate disorder below the putative MBL transition, NLCE outperforms direct simulations of finite systems with open or periodic boundaries. Furthermore, while spin is delocalized even in strongly disordered Hubbard chains with frozen charge, we unveil that an additional tilted potential leads to a drastic slowdown of the spin imbalance and nonergodic behavior on accessible times. Our work sheds light on MBL in systems beyond the well-studied disordered Heisenberg chain and emphasizes the usefulness of NLCE for this purpose.