The Density Matrix Renormalization Group Studies of Metal-Halogen Chains   within a Two-Band Extended Peierls-Hubbard Model
  The phase diagram of halogen-bridged mixed-valent metal complexes ($MX$) has been studied using a two-band extended Peierls-Hubbard model employing the recently developed Density Matrix Renormalization Group method. We present the energies, charge and spin density distributions, bond orders, charge-charge and spin-spin correlations, in the ground state for different parameters of the model. The effect of bond alternation and site-diagonal distortion on the ground state properties are considered in detail. We observe that the site-diagonal distortion plays a significant role in deciding the nature of the ground state of the system. We find that while the $CDW$ and $BOW$ phases can coexist, the $CDW$ and $SDW$ phases are exclusive in most of the cases. We have also studied the doped $MX$ chains both with and without bond alternation and site-diagonal distortion in the $CDW$ as well as $SDW$ regimes. We find that the additional charge in the polarons and bipolarons for hole doping are confined to a few sites, in the presence of bond alternation and site-diagonal distortion. For electron doping, we find that the additional charge(s) is(are) smeared over the entire chain length and although energetics imply a disproportionation of the negatively charged bipolaron, the charge and spin density distributions do not reflect it. Positively charged bipolaron disproportionates into two polarons in the $SDW$ region. There is also bond order evidence for compression of bond length for the positively charged polaronic and bipolaronic systems and an elongation of the bonds for systems with negatively charged polarons and bipolarons. 
Y. Anusooya, Swapan K Pati and S. Ramasesha