Discovering Quantum Phase Transitions with Fermionic Neural Networks

Deep neural networks have been very successful as highly accurate wave function ansatze for variational Monte Carlo calculations of the ground states of solids and molecules. We demonstrate that deep neural network ansatze with identical architectures are capable of representing quantum phases with completely distinct qualitative characteristics. We investigate the ground-state wavefunction of the homogeneous electron gas either side of the famed Wigner transition using the Fermionic neural network (FermiNet) architecture. Without any hand-crafted features indicating the presence of a phase transition, the neural network correctly converges to a crystalline state at low density and a gaseous state at high density. We stress that this is a unique advantage of neural approaches which do not depend upon basis functions: traditional electronic structure methods require the selection of a basis which is appropriate for the qualitative nature of the phase being studied, hindering the study of hitherto unknown phases. Our results suggest variational calculations with deep neural network wavefunction ansatze could be used to detect unforseen quantum phase transitions, or discover new phases of quantum matter. In this talk, I will discuss the present limitations of the method and provide perspectives on future research.