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The impact of local reflection symmetry on wave localization and transportwithin finite disordered chains is investigated. Local symmetries thereby playthe role of a spatial correlation of variable range in the finite system. Wefind that, on ensemble average, the chain eigenstates become more fragmentedspatially for intermediate average symmetry domain sizes, depending on thedegree of disorder. This is caused by the partial formation of states withapproximate local parity confined within fictitious, disorder-induced doublewells and perturbed by the coupling to adjacent domains. The dynamicalevolution of wave-packets shows that the average site-resolved transferefficiency is enhanced between regions connected by local symmetry. Thetransfer may further be drastically amplified in the presence of spatialoverlap between the symmetry domains, and in particular when global and localsymmetry coexist. Applicable to generic discrete models for matter and lightwaves, our work provides a perspective to understand and exploit the impact oflocal order at multiple scales in complex systems.

Transfer efficiency enhancement and eigenstate properties in locally symmetric disordered finite chains