“Equipartition & Entanglement”.Relation between ergodicity measures

by Dr Ivan Khaymovich (Nordita)

Thursday 22 Sept 2022, 13:00 → 15:00 Europe/Stockholm

AlbaNova C4:3059 - Café Planck (AlbaNova Main Building)

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 {\it 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.