Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space

We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid He4 in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation to zero variance gives energies in close agreement with the exact values. For two dimensional He4, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form - a feature shared with the shadow wave function, but now joined by much higher accuracy. We also achieve significant progress for liquid He3 in three dimensions, improving previous variational and fixed-node energies. © 2018 American Physical Society.