Implementation of the linear method for the optimization of Jastrow-Feenberg and backflow correlations

We present a fully detailed and highly performing implementation of the Linear Method (Toulouse and Umrigar, 2007) to optimize Jastrow-Feenberg and Backflow Correlations in many-body wave-functions, which are widely used in condensed matter physics. We show that it is possible to implement such optimization scheme performing analytical derivatives of the wave-function with respect to the variational parameters achieving the best possible complexity O(N3) in the number of particles N.