Dresden 2020 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 5: Many-body Systems: Equilibration, Chaos and Localization I (joint session DY/TT)
DY 5.3: Talk
Monday, March 16, 2020, 10:45–11:00, HÜL 186
Entanglement entropy of fractal states — •Giuseppe De Tomasi1 and Ivan Khaymovich2 — 1Department of Physics, T42, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany — 2Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187-Dresden, Germany
In this talk we will discuss the relations between entanglement (and Renyi) entropies and fractal dimensions Dq of many-body wave-functions.
As a simple example we introduce a new class of sparse random pure states being fractal in the corresponding computational basis and show that their entropies grow linearly with for fractal dimension smaller than the subsystem size (Dq<0.5 for equipartitioning) and reach the upper bound of Page value otherwise, far below the ergodic limit Dq = 1. The latter shows that Page value entanglement entropy does not guarantee ETH.
Moreover this Dq-dependence poses an upper bound for entanglement and Renyi entropies of any multifractal states and uncovers the relation between multifractality and entanglement properties of many-body wave-functions.