# Localization in the droplet spectrum of the random XXZ quantum spin chain

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We study the XXZ quantum spin chain in a random field. This model is particle number preserving, which allows the reduction to an infinite system of discrete many-body random Schrodinger operators. We exploit this reduction to prove a form of Anderson localization in the droplet spectrum of the XXZ quantum spin chain Hamiltonian. This yields a strong form of dynamical exponential clustering for eigenstates in the droplet spectrum: For any pair of local observables, the sum of the associated correlators over these states decays exponentially in the distance between the local observables. Moreover, this exponential clustering persists under the time evolution in the droplet spectrum.