Peierls-Hubbard dimer

FIG. 1. Energy levels, transition dipoles, and electron-vibration (Herzberg-Teller) couplings in the symmetric Peierls-Hubbard dimer. 

Monte Carlo simulations [17, 18], the valence bond approach [19, 20], and g-ology [21-24] indicate that the Peierls instability in half-filled chains survives the presence of electron-electron interactions (at least, for some range of interaction parameters). This holds for a variety of different models, such as the Peierls-Hubbard model with the onsite Coulomb repulsion, or the Pariser-Parr-Pople model, where also long-range Coulomb interactions are taken into account ]2]. As the dimerization persists in the presence of electron-electron interactions, also the soliton concept survives. An important difference with the SSH model is that neu-... 

This note is organized as follows. In section II, the RVA is presented using the example of the two-legspin ladders. In section III, the RVA method is applied to the study of the dimerized chain described by the Extended Peierls-Hubbard model. A nice similarity between the two-leg ladder and this system is pointed out and comparisons with DMRG calculations are made. We conclude in section IV and give some reasonable perspectives. 

Let us now introduce the electron-vibration interaction in the symmetric dimer, to account for the modulation of the site energies, and of the electron transfer integral, by the intramolecular vibrational modes and by the rigid molecular motions respectively. This leads us to the so-called Peierls—Hubbard model. ... 

In the case of the CP state, where an unpaired electron exists at the M " site per dimer unit, no cell doubling occurs and so either a Mott-Hubbard insulator or a one-dimensional metal is expected. Conversely, the electronic structures of the CDW state and the ACP state are regarded as Peierls and spin-Peierls states, respectively [178,184,185]. The four states of the MMX complexes are distinguished by the valence states of the metal and the bond distances in the crystal structure. 

The parameters should be compared with the bandwidth, i.e. with the longitudinal transfer integral t in pseudo-1-D systems. Since, in the presence of a weak dimerization, the Peierls gap is negligible (compared to the Hubbard gap), therefore, for regular or pseudo-regular stacking, the following requirement appears to be necessary ... 

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