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Disorder-Free Many-Body Localization via Fractal Coupling at α = 2.1875 = 35/16: Experimental Discovery on IBM Quantum Hardware and the VecFrachZ Crystal

Guacalita Inc., Jose GOMEZ

Published Sep 2, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.22246319

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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.
The space of one-dimensional disordered interacting quantum models displaying a many-body localization (MBL) transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the localized phase and the Wigner–Dyson statistics of the delocalized phase. In this paper, we consider the strong disorder limit of the MBL transition, where the level statistics at the MBL critical point is close to the Poisson statistics. We analyze a one-dimensional quantum spin model, in order to determine the statistical properties of the rare extensive resonances that are needed to destabilize the MBL phase. At criticality, we find that the entanglement entropy can grow with an exponent 0 < α < 1 anywhere between the area law α = 0 and the volume law α = 1 , as a function of the resonances properties, while the entanglement spectrum follows the strong multifractality statistics. In the MBL phase near criticality, we obtain the simple value ν = 1 for the correlation length exponent. Independently of the strong disorder limit, we explain why, for the many-body localization transition concerning individual eigenstates, the correlation length exponent ν is not constrained by the usual Harris inequality ν ≥ 2 / d , so that there is no theoretical inconsistency with the best numerical measure ν = 0 . 8 ( 3 ) obtained by Luitz et al. (2015).
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.
We investigate the occurrence of the phenomenon of many-body localization (MBL) on a D-Wave 2000Q programmable quantum annealer. We study a spin-1/2 transverse-field Ising model defined on a Chimera connectivity graph, with random exchange interactions and random longitudinal fields. On this system we experimentally observe a transition from an ergodic phase to an MBL phase. We first theoretically show that the MBL transition is induced by a critical disorder strength for individual energy eigenstates in a Chimera cell, which follows from the analysis of the mean half-system block entanglement, as measured by the von Neumann entropy. We show the existence of an area law for the block entanglement over energy eigenstates for the MBL phase, which stands in contrast with an extensive volume scaling in the ergodic phase. The identification of the MBL critical point is performed via the measurement of the maximum variance of the mean block entanglement over the disorder ensemble as a function of the disorder strength. Our results for the energy density phase diagram also show the existence of a many-body mobility edge in the energy spectrum. The time-independent disordered Ising Hamiltonian is then experimentally realized by applying the reverse annealing technique allied with a pause-quench protocol on the D-Wave device. We then characterize the MBL critical point through magnetization measurements at the end of the annealing dynamics, obtaining results compatible with our theoretical predictions for the MBL transition.
The failure of quantum thermalization due to Many-Body Localization (MBL) has evolved from a theoretical concept in spin chains to an experimental reality in synthetic quantum platforms, most notably superconducting circuits based on transmon qubits. Despite its significance, the MBL transition has been studied primarily under purely random disorder and local couplings, leaving more complex and realistic configurations largely unexplored. Here, we investigate the quantum dynamics of transmon networks subject to the unavoidable competing effects of correlated disorder and network-mediated non-local interactions. First, we show how to engineer the physical parameters of the quantum hardware to systematically control the correlated disorder patterns emerging in the system. Then, we demonstrate that the MBL phase transition is robust against such correlations, which is essential for tuning localization properties in realistic transmon devices. This robustness is established through the analysis of the block entanglement entropy variance across disorder realizations, which precisely locates the MBL critical point. Independently, we introduce a local memory parameter, whose dynamics at long evolution times reveals memory retention in the localized phase and yields a critical point consistent with the entropy analysis. These results provide a framework for understanding localization in complex quantum network topologies, with potential implications for multi-qubit processor design.
We review recent results on many-body localization for two explicitly analyzable models of many-body quantum systems, the XY spin chain in transversal magnetic field as well as interacting systems of harmonic quantum oscillators. In both models the presence of disorder leads to dynamical localization in the form of zero-velocity Lieb-Robinson bounds and to exponential decay of ground state correlations. Moreover, for oscillator systems one can also show exponential decay of thermal states as well as an area law bound for the entanglement entropy of ground and thermal states. The key fact which allows a rigorous analysis of these models is that they are given by many-body Hamiltonians which can be reduced to effective single particle Hamiltonians.
Disorder free many-body localization (MBL) can occur in interacting systems that can dynamically generate their own disorder. We address the thermal-MBL phase transition of two isotropic Heisenberg spin chains that are quasiperiodically coupled to each other. The spin chains are incommensurate and are coupled through a short-range exchange interaction of the X X Z type that decays exponentially with the distance. Using exact diagonalization, matrix product states, and a density matrix renormalization group, we calculate the time evolution of the entanglement entropy at long times and extract the inverse participation ratio in the thermodynamic limit. We show that this system has a robust MBL phase. We establish the phase diagram with the onset of MBL as a function of the interchain exchange coupling and of the incommensuration between the spin chains. The Ising limit of the interchain interaction optimizes the stability of the MBL phase over a broad range of incommensurations above a given critical exchange coupling. Incorporation of interchain spin flips significantly enhances entanglement between the spin chains and produces delocalization, favoring a prethermal phase whose entanglement entropy grows logarithmically with time. Published by the American Physical Society 2024