Dresden 2020 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 9: Many-body Systems: Equilibration, Chaos and Localization I (joint session DY/TT)

TT 9.3: Vortrag

Montag, 16. März 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 D_q 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 (D_q<0.5 for equipartitioning) and reach the upper bound of Page value otherwise, far below the ergodic limit D_q = 1. The latter shows that Page value entanglement entropy does not guarantee ETH.

Moreover this D_q-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.