# Talk:Gutzwiller wave function/historical note

It is a good idea to write such an article. Still, I feel that there are a number of issues that can be improved:

-I did not like the discussion of the H molecule. The authors call the two site Hubbard model an H-molecule. One should at least comment on the fact that only 1s states are included and that the inter-atomic interactions have been fully ignored. After all the latter cause the binding of the molecule. A motivating example should be relevant. For the non-expert reader this discussion should be made clearer, otherwise he/she stop reading right away...

-I would love to see an explicit discussion of Eq.1 for a toy model (say the two site problem). Why not write down the states with their weights, analyze kinetic and potential energy, stress that one increases with g the other decreases and show that a compromise leads to a local minimum. Then a reader 'sees' what is meant by Eq.(1). This is more important than the rather formalistic generalization to multiple orbitals etc. etc.

-On "Exact results in one spatial dimension". Please add a comment why the solution in d=1 is possible and how it compares with exactly known results (in addition to plotting the energies). Is the discontinuity at kF a sensible result or not? What do we learn? The same holds for infinite dimensions.

-On "Evaluation": The Variational Monte Carlo approach is not even mentioned here. This is the most powerful method to evaluate the GW wave function (without the GW-approx.). It allows to simulate a quantum many body system on the computer as if it was a classical system. Also, it was hugely important in the context of the Resonating Valence Bond theory of frustrated magnets and cuprates. A review should address this.

-On the Historical note: The current version is much improved over what I saw about 2 weeks ago. The specific model was independently proposed by Gutzwiller, Hubbard, and Kanamori. It has had a huge impact in the field. One of the three 'inventors' of the model is a coauthor of this review. If he wants to share anecdotes that led to the model (and/or to his wave functions) with us, here is an opportunity. Which ideas didn't work, but inspired this pioneering paper? What motivated the GW approximation? etc.