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

TL;DR

This paper demonstrates that higher-dimensional models with symmetric correlated hoppings exhibit localization due to fragmentation and possess boundary charges with long-lived correlations, extending concepts of zero modes beyond one dimension.

Contribution

It provides a rigorous proof of localization in higher dimensions and constructs boundary conserved quantities, advancing understanding of boundary phenomena in complex quantum systems.

Findings

Models exhibit localization due to fragmentation in any dimension

Boundary charges are conserved and long-lived

Construction of higher-dimensional strong zero modes

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.