Backflow orbital

First, how do the particles move in VMC In the continuum it is usually more efficient to move the particles one at a time by adding a random vector to a particle s coordinate, where the vector is either uniform inside of a cube, or is a normally distributed random vector centered around the old position. Unfortunately, this procedure cannot be used with backflow orbitals. This is because the backflow transformation couples all the electronic coordinates in the orbitals so that once a single electron move is attempted the entire Slater determinant needs to be recomputed, an 0 N ) operation. It is much more efficient to move all electrons at once, although global moves could become inefficient for large systems. 

Fig. 2. Ne = Np = 16, Vs = 1.31. Dependence of total energy, variance and energy difference for a pair of proton configurations S, S ) on the RQMC projection time. The study is performed for Te = 0.02Dotted lines represent the variational estimates with their error bars. In panel b) and c) the lines are exponential fits to data and in panel d) the continnons line is a linear fit in the region < 0.005. Black circles (3BF-A) are resnlts obtained with the analitical three-body and backflow trial wave functions discnssed earlier, the red triangle is a variational resnlt with a Slater-Jastrow trial function with simple plane wave orbitals and the blue squares are results from a trial function with LDA orbitals and an optmized two-body Jastrow...

Yet another approach to incorporating correlation effects into an antisymmetric function is to allow the orbitals (or geminals) to depend on the coordinates of the other electrons. This is accomplished by the backflow transformation in which the coordinates of the electrons are modified by a backflow displacement ... 

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