Effects of Short-Range Interactions on Electron-Charge Ordering and Lattice Distortions in the Localized State

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Abstract
We investigate the role of electron-lattice interactions in a very narrow half-filled band that would otherwise be described as a Mott insulator. A simple Hamiltonian is presented that incorporates the electron-electron and electron-lattice interactions in the zero-overlap limit. A canonical transformation decouples the electron and lattice systems and we assume that the effective electron-electron interaction is short ranged. It is found that, within an approximation that treats intra-atomic correlations exactly, the Mott insulator can undergo a phase transition to a quite different insulating state as the temperature is lowered. This insulating state is characterized by a charge-density wave in which alternate atomic sites are doubly occupied as opposed to the usual one-electron-per-atom configuration in the Mott state. The phase transition will be either first or second order, depending on the electronlattice coupling strength. Accompanying the charge-ordered state is a distortion of the crystal lattice that lowers its translational symmetry.

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