Correlation mediated superconductivity in a Spin Peierls phase of the Hubbard model

Abstract

We explore the consequences of a mapping of the Hubbard Hamiltonian with a view to finding possible superconducting phases. The transformation pairs up all the sites and is therfore a much more natural starting point for describing a “Spin Peierls” transition, generating enhanced singlet correlations for this pairing, than it is for describing the “Resonating Valence Bond” (RVB) state of Anderson. We show that in the less than half filling case, an effective non-linear hopping Hamiltonian is quite useful in describing half of the electrons. This effective Hamiltonian can show a form of superconducting instability when nearest neighbour hopping is introduced to stabilise it. This superconducting phase seems to be a very unlikely possibility for the standard Hubbard model.