Conclusions and where do we stand
- A simple extension of the work of G. Carleo and M. Troyer, Science 355, Issue 6325, pp. 602-606 (2017) gives excellent results for two-electron systems as well as good agreement with standard VMC calculations for \( N=6 \) and \( N=12 \) electrons.
- Minimization problem can be tricky.
- Anti-symmetry dealt with multiplying the trail wave function with an optimized Slater determinant.
- To come: Analysis of wave function from ML and compare with diffusion and Variational Monte Carlo calculations as well as the analytical results of Taut for the two-electron case.
- Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function?
- Here we used standard Hartree-Fock theory to define an optimal Slater determinant. Takes care of the antisymmetry. What about constructing an anti-symmetrized network function?
- Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor).
- Test this for multi-fermion systems and compare with other many-body methods.
- Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories?