Resonating valence bond theory. The approach from weak coupling

Very soon after the discovery of the high-Tc cuprate superconductors Anderson proposed the key to understanding their highly unusual properties lay in the ansatz that they were hole doped spin liquids in which the spins are bound in singlet pairs resonating between different configurations. This RVB concept is generally formulated for a doped Mott insulator, i.e. for a system with a strong onsite Coulomb interaction. It is instructive to explore the approach from weak Coulomb interaction to see if similar behavior can also occur in this case. Quasi-one dimensional systems in the form of finite width ladders do indeed show such behavior with a continuous crossover from weak to strong interaction limits. In two dimensions functional renormalization group methods have recently been developed to treat weak to moderately strong interactions. These show that similar behavior can occur in the case that the Fermi energy lies near the logarithmically divergent van Hove singularity in the density of states when the band is nearly half-filled. These methods are limited to a description of the flow to strong coupling as the energy or temperature scale is lowered. The form of the strong coupling phase can be explored by numerical techniques. However a proper theory of this phase is lacking and even a consistent phenomenological description has not yet been achieved. (author)