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We show how a ground state trial wavefunction of a Fermi liquid can besystematically improved introducing a sequence of renormalized coordinatesthrough an iterative backflow transformation. We apply this scheme to calculatethe ground state energy of liquid $^3$He in two dimensions at freezing densityusing variational and fixed-node diffusion Monte Carlo. Comparing with exacttransient estimate results for systems with small number of particles, we findthat variance extrapolations provide accurate results for the true ground statetogether with stringent lower bounds. For larger systems these bounds can inturn be used to quantify the systematic bias of fixed-node calculations. Thesewave functions are size consistent and the scaling of their computationalcomplexity with the number of particles is the same as for standard backflowwave functions.

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