Statistical localization: From strong fragmentation to strong edge modes Article Swipe
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· 2020
· Open Access
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· DOI: https://doi.org/10.1103/physrevb.101.125126
· OA: W2980324323
Certain disorder-free Hamiltonians can be non-ergodic due to a \\emph{strong\nfragmentation} of the Hilbert space into disconnected sectors. Here, we\ncharacterize such systems by introducing the notion of `statistically localized\nintegrals of motion' (SLIOM), whose eigenvalues label the connected components\nof the Hilbert space. SLIOMs are not spatially localized in the operator sense,\nbut appear localized to sub-extensive regions when their expectation value is\ntaken in typical states with a finite density of particles. We illustrate this\ngeneral concept on several Hamiltonians, both with and without dipole\nconservation. Furthermore, we demonstrate that there exist perturbations which\ndestroy these integrals of motion in the bulk of the system, while keeping them\non the boundary. This results in statistically localized \\emph{strong zero\nmodes}, leading to infinitely long-lived edge magnetizations along with a\nthermalizing bulk, constituting the first example of such strong edge modes in\na non-integrable model. We also show that in a particular example, these edge\nmodes lead to the appearance of topological string order in a certain subset of\nhighly excited eigenstates. Some of our suggested models can be realized in\nRydberg quantum simulators.\n
