SKM 2021 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 2: Quantum Chaos

DY 2.7: Talk

Tuesday, September 28, 2021, 12:00–12:15, H6

Emergent fractal phase in energy stratified random models — •Anton Kutlin and Ivan Khaymovich — Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187-Dresden, Germany

We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson's model and the celebrated Rosenzweig-Porter model (with implemented translation-invariant symmetry). In order to do this, we propose the energy-stratified spectral structure of the hopping term, allowing one to gradually decrease the range of correlations. We show both analytically and numerically that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system unlike the predictions of localization of cooperative shielding. In order to describe the models with correlated kinetic terms, we develop the generalization of the Dyson Brownian motion and cavity approaches basing on stochastic matrix process with independent rank-one matrix increments and examine its applicability to the above set of models