# Dresden 2020 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 23: Nonequilibrium Quantum Many-Body Systems 1 (joint session TT/DY)

### TT 23.12: Vortrag

### Dienstag, 17. März 2020, 12:30–12:45, HSZ 204

**Statistical localization: from strong fragmentation to strong edge modes** — •Tibor Rakovszky^{1}, Pablo Sala^{1}, Ruben Verresen^{2}, Michael Knap^{1}, and Frank Pollmann^{1} — ^{1}Department of Physics, Technical University of Munich, 85748 Garching, Germany — ^{2}Department of Physics, Harvard University, Cambridge, MA 02138, USA

Certain disorder-free Hamiltonians can be non-ergodic due to a strong fragmentation of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of "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 when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation. Furthermore, we demonstrate 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 show that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigenstates. Some of our suggested models can be realized in Rydberg quantum simulators.