Phase diagram of helium-4 in two dimensions using neural quantum states

We explore the phase diagram of helium-4 confined to two spatial dimensions at zero temperature, using a neural quantum state trial wavefunction. Using the same symmetric and translationally invariant functional form, we are able to accurately describe phases of different spatial symmetries (liquid and solid), as well as the phenomena of Bose-Einstein condensation. In contrast to previous quantum monte carlo studies, the accuracy of our description allows us for the first time to perform fixed-pressure simulations to properly address the liquid-solid phase transition as well as possible intermediate exotic phases. Whereas our simulations of small cells reveal some sign of hexatic and supersolid behaviors, simulations of larger systems indicate strong finite-size bias, questioning the appearance of these exotic phases in the thermodynamic limit. We further show that the entanglement entropy of the liquid grows with pressure, dropping significantly at the transition to the solid state.