Electronic states, Mott localization, electron-lattice coupling, and dimerization for correlated one-dimensional systems. II

We discuss physical properties of strongly correlated electron states for a linear chain obtained with the help of the recently proposed new method combining the exact diagonalization in the Fock space with an ab initio readjustment of the single-particle orbitals in the correlated state. The method extends the current discussion of the correlated states since the properties are obtained with varying lattice spacing. The finite system of N atoms evolves with the increasing interatomic distance from a Fermi-liquid-like state into the Mott insulator. The criteria of the localization are discussed in detail since the results are already convergent for N>=8. During this process the Fermi-Dirac distribution gets smeared out, the effective band mass increases by ~50%, and the spin-spin correlation functions reduce to those for the Heisenberg antiferromagnet. Values of the microscopic parameters such as the hopping and the kinetic-exchange integrals, as well as the magnitude of both intra- and inter-atomic Coulomb and exchange interactions are calculated. We also determine the values of various local electron-lattice couplings and show that they are comparable to the kinetic exchange contribution in the strong-correlation limit. The magnitudes of the dimerization and the zero-point motion are also discussed. Our results provide a canonical example of a tractable strongly correlated system with a precise, first-principle description as a function of interatomic distance of a model system involving all hopping integrals, all pair-site interactions, and the exact one-band Wannier functions.