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Fragmentation-induced localization and boundary charges in dimensions two and above

by Julius Lehmann, Pablo Sala de Torres-Solanot, Frank Pollmann, Tibor Rakovszky

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Authors (as registered SciPost users):

Julius Lehmann · Tibor Rakovszky · Pablo Sala de Torres-Solanot

Abstract

We study higher dimensional models with symmetric correlated hoppings, which generalize a one-dimensional model introduced in the context of dipole-conserving dynamics. We prove rigorously that whenever the local configuration space takes its smallest non-trivial value, these models exhibit localized behavior due to fragmentation, in any dimension. For the same class of models, we then construct a hierarchy of conserved quantities that are power-law localized at the boundary of the system with increasing powers. Combining these with Mazur's bound, we prove that boundary correlations are infinitely long lived, even when the bulk is not localized. We use our results to construct quantum Hamiltonians that exhibit the analogues of strong zero modes in two and higher dimensions