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
The authors addressed all the issues. I think the paper satisfies all the criteria for publication in SciPost Physics. I am happy to recommend it for publication.
Alexey Khudorozhkov on 2023-02-22 [id 3390]
The authors addressed all the issues. I think the paper satisfies all the criteria for publication in SciPost Physics. I am happy to recommend it for publication.