Electron Correlations, Magnetic Ordering, and Mott Insulation in Solids

Abstract

A model is constructed for the purpose of investigating electron correlations pertinent to magnetic ordering and Mott insulation in solids. The model consists of an assembly of interacting itinerant electrons in a periodic atomic lattice, such that the intra‐atomic coupling between electrons is extremely strong. The correlations due to this latter coupling serve to prevent electrons of opposite spin from occupying the same atomic state, except in virtual transitions. Thus their net effect is to renormalize certain interactions and, also, to confine the state vectors of the entire system to a subspace, $\mathfrak{H},$ of the Hilbert space, ${\mathfrak{H}}_0,$ that is kinematically available to them. The observables are thus represented by operators on $\mathfrak{H},$ whose algebraic properties are different from thsoe of the corresponding operators on ${\mathfrak{H}}_0.$ Thus, the correlations due to intra‐atomic forces are imbedded in the theory in the form of the new algebra. In cases of one electron per atom, these correlations lead simply to both magnetic ordering and Mott insulation. In cases of nonintegral number of electrons per atom, they can lead to magnetic ordering, subject to specified conditions.