Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids

We show how a ground state trial wavefunction of a Fermi liquid can be systematically improved introducing a sequence of renormalized coordinates through an iterative backflow transformation. We apply this scheme to calculate the ground state energy of liquid $^3$He in two dimensions at freezing density using variational and fixed-node diffusion Monte Carlo. Comparing with exact transient estimate results for systems with small number of particles, we find that variance extrapolations provide accurate results for the true ground state together with stringent lower bounds. For larger systems these bounds can in turn be used to quantify the systematic bias of fixed-node calculations. These wave functions are size consistent and the scaling of their computational complexity with the number of particles is the same as for standard backflow wave functions.