Department of Physics • University of Cologne

Neural networks offer a novel approach to represent wave functions for solving quantum many-body problems. It is of both theoretical interests and practical use to know what kinds of quantum states are efficiently represented by neural networks. In this talk, we will address this question from a new perspective from statistical mechanics by considering the ensemble property of random neural network quantum states. We show that these states are generically volume-law entangled and multifractal. Furthermore, depending on network parameters, there are entanglement phase transitions where one of the phases, despite being still non-ergodic, can reach nearly maximal entanglement.