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Seminar Physique Math茅matique
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Title: Hilbert Space Fragmentation

Abstract:Strong interactions and frustration often lead to dynamically constrained excitations of quantum matter. Examples include spin-ice compounds whose spin moments are aligned to fulfill a local ice rule, frustrated quantum magnets with dimerized excitations, and fracton phases with excitations that are only mobile in certain directions if at all. Here, we will discuss that the combination of charge and dipole conservation, a characteristic of fractonic quantum matter, leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization. We characterize such a Hilbert space fragmentation by introducing `statistically localized integrals of motion' (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to sub-extensive regions in space when their expectation value is taken in typical states with a finite density of particles. Furthermore, we discuss that there exist perturbations which destroy these integrals of motion in the bulk of the system, while keeping them on the boundary. This results in statistically localized strong zero modes, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk, constituting the first example of such strong edge modes in a non-integrable model. We also discuss that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigen states. A variant of these models can be realized in Rydberg quantum simulators.