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We demonstrate strong non-ergodic behavior in the XY model on coupled chains, where domain-wall initial states retain an inhomogeneous magnetization profile for arbitrarily long times. We find that this effect arises due to zero modes protected by chiral symmetry. Using an analysis based on the Lanczos algorithm, we identify evidence for a localization transition in the thermodynamic limit at a critical coupling between the chains. We further show that antiferromagnetic defects in the initial state and symmetry-breaking perturbations restore slow thermalization, whereas it remains robust for symmetry-conserving perturbations. These results establish that degenerate, symmetry-protected subspaces can give rise to thermodynamically stable non-ergodic dynamics in experimentally accessible quantum systems [1].
[1] P. Kos, D. S. Wild, and K. Knakkergaard Nielsen, arXiv:2604.15510 (accepted for publication in Phys. Rev. Letters).