For short-range perturbations of gapped one-dimensional quantum chains with unbounded on-site terms, a positive spectral gap (at least 1/2) persists uniformly in system size for sufficiently small coupling.
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Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions
For short-range perturbations of gapped one-dimensional quantum chains with unbounded on-site terms, a positive spectral gap (at least 1/2) persists uniformly in system size for sufficiently small coupling.