Recent advances in the study of frustrated magnetism with Neural-Network quantum states

Neural-Network quantum states are an actively explored route to solve challenging interacting quantum problems.
Early representations of many-body quantum states in terms of artificial neural networks were based on shallow, restricted Boltzmann Machines [1-3]. The benefits of using deeper networks are however emerging in latest research, where the use of suitably adapted deep networks to the quantum domain is proving rewarding.
During this talk I will discuss our strategy to represent quantum states using deep convolutional networks.
The advantages of this representation will be shown in the particularly challenging case of frustrated magnets in two dimensions. Here, I will show latest applications to the frustrated J1-J2 model on the square lattice. In this case, neural-network quantum states achieve results that are comparable or better than existing state of the art variational methods developed in the past decade.
[1] Carleo and Troyer, Science 355, 602 (2017) [2] Torlai et al, Nature Physics 14, 447-450 (2018) [3] Jónsson, Bauer, and Carleo arXiv:1808.05232 (2018)