Title: Nonlinear Network description for many-body quantum systems in continuous space,
Abstract: We show that the recently introduced iterative backflow renormalization can
be interpreted as a general neural network in continuum space with non-linear
functions in the hidden units. We use this wave function within Variational
Monte Carlo for liquid $^4$He in two and three dimensions, where 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 of these energies to zero variance
gives values 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 for this very
challenging fermionic system.