Long-Range Correlated Quantum States 
from Artificial Neural Networks

Artificial neural networks and machine learning tools have become ubiquitous far beyond the field of computer science, and already smartly assist us in our daily lives in various ways. Recently, these concepts have been adopted and applied in the realm of quantum physics, for example as a variational ansatz for the state of a quantum many-body system. In this talk, we discuss our recent results on long-range correlated neural network quantum states that exhibit entanglement properties beyond the area law scaling familiar from tensor network states. As concrete case studies, we show how certain chiral topological phases can be efficiently represented in the framework of artificial neural networks, and we propose a constructive extension of matrix product states that is promising for the study of dynamical and critical low-dimensional systems.