Reduced Density Matrices for Valence Bond Wavefunctions. III. Density Matrices for the 4×4 Square Planar Net
Jong H. Choi, Walter R. Thorson
One- and two-particle reduced density matrices have been calculated for a ``resonating'' Heitler-London wavefunction, in a system which is a finite model of a two-dimensional square planar lattice structure (4×4 net of one-electron atoms with Born-von Karman boundary conditions). The Heitler-London wavefunction describes the electronic ground state of a system with a single narrow half-filled band (the Mott insulator). Various measures of electron correlation (pair correlation functions, etc.) are defined and calculated. The intent of these calculations is to provide ``empirical'' guidelines for many-body methods for calculation of Green's functions for one and two particles (reduced density matrices are initial values for the respective Green's functions). Results show that the Heitler-London description is incompatible with several assumptions and widely used models for the Mott insulator. In particular it is found that (a) pair correlations in the Heitler-London ground state remain local even when ``resonance'' of an extremely large number of valence-bond structures occurs; the long range antiferromagnetic ordering obtained in several models of the Mott insulator (the ``two-sublattice'' or ``different bands for different spins'' models) does not occur. (b) The density matrix for the Heitler-London state does not exhibit a BCS type ``pair condensation'', as has been conjectured to describe the Mott insulator in some recent work. Our results strongly suggest that if the Heitler-London description is appropriate, the ``Hubbard Hamiltonian'', which includes only intraatomic pair interactions, does not offer an adequate model of the Mott insulator.
The Journal of Chemical Physics•Jul 1, 1972•12 citations