Competing ground states of metal-halide ladders

Based on a symmetry argument, we investigate the ground-state properties of newly synthesized metal-halide ladder compounds (C_8_H_6_N_4_)[Pt(C_2_H_8_N_2_)X]2(ClO_4_)4 2H_2_O (X=Cl, Br, I). Employing a fully dressed two-band Peierls-Hubbard model, we systematically reveal possible charge- or spin-ordered states. Numerical phase diagrams demonstrate a variety of competing Peierls and Mott insulators with particular emphasis on the transition between two types of mixed-valent state of Pt^II^ and Pt^IV^ driven by varying interchain hopping integrals and Coulomb interactions.