In 1987 Anderson originally proposed his RVB wave function (a Gutzwiller projected BCS wave function) as the ground state of the Heisenberg model on the square lattice. This turned out to be a poor guess. This state has zero magnetic moment and an energy 5 per cent larger than the true ground state energy. It has an overlap of about 0.8 with the true ground state (on a finite lattice). This led many (including me) to discount the relevance of RVB to quantum magnetism and particularly superconductivity. However, I changed my mind about seven years ago when I saw figures such as those below from Federico Becca, Sandro Sorella, and collaborators. (The figure is taken from a nice set of lecture notes that they recently wrote).

They show how an RVB wave functions becomes more reliable as the frustration increases for the case of the frustrated Heisenberg model (the J1-J2 model) on the square lattice. The upper panel shows the energy difference between a projected BCS wave function and the exact ground state for a lattice of 6 x 6 sites. The lower panel shows the overlap of these two states.

I think the overlap plot is particularly important. As they're doing a variational method they're almost guaranteed to get a reasonable energy. But getting a good overlap (ie the right physics) is a very different story.

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