Resonating valence bond theory

The RVB state with valence bond coupling of nearest-neighbor electrons.

The physics of Mott insulators is described by the repulsive Hubbard model Hamiltonian:

${\displaystyle H=-t\sum _{\langle ij\rangle }(c_{i\sigma }^{\dagger }c_{j\sigma }+{\text{h.c.}})+U\sum _{i}n_{i\uparrow }n_{i\downarrow }}$

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

${\displaystyle |{\text{RVB}}\rangle =\sum _{C}|C\rangle }$

where ${\displaystyle C}$ 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]