In 2014, evidence showing that fractional particles can happen in quasi two-dimensional magnetic materials, was found by EPFL scientists[5] lending support for Anderson's theory of high-temperature superconductivity.[6]
In 1971, Anderson first suggested that this Hamiltonian can have a non-degenerate ground state that is composed of disordered spin states. Shortly after the high-temperature superconductors were discovered, Anderson and Kivelson et al. proposed a resonating valence bond ground state for these materials, written as
where represented a covering of a lattice by nearest neighbor dimers. Each such covering is weighted equally. In a mean field approximation, the RVB state can be written in terms of a Gutzwiller projection, and displays a superconducting phase transition per the Kosterlitz–Thouless mechanism.[7] However, a rigorous proof for the existence of a superconducting ground state in either the Hubbard or the t-J Hamiltonian is not yet known.[7] Further the stability of the RVB ground state has not yet been confirmed.[8]