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 ^{4}He 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 ^{4}He, 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 ^{3}He in three dimensions, improving previous variational and fixed-node energies.

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