SKM 2021 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 11: Focus Session: Facets of Many-Body Quantum Chaos (organised by Markus Heyl and Klaus Richter) (joint session DY/TT)

TT 11.6: Talk

Wednesday, September 29, 2021, 11:15–11:30, H6

Entanglement entropy of fractal states — Giuseppe De Tomasi¹ and •Ivan Khaymovich² — ¹T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom — ²Max Planck Institute for the Physics of Complex Systems

In this talk we will discuss the relations between entanglement (and Renyi) entropies and fractal dimensions D_q of many-body wavefunctions.

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 reach the upper bound of Page value for fractal dimension larger than the subsystem size (D_q>0.5 for equipartitioning) and grow linearly with D_q otherwise.

Moreover this dependence poses the upper bound for entanglement and Renyi entropies for any multifractal states and uncovers the relation between multifractality and entanglement properties of many-body wavefunctions.