Competing Ground States of a Peierls-Hubbard Nanotube

Motivated by iodo platinum complexes assembled within a quadratic-prism lattice, [Pt(C$_2$H$_8$N$_2$)(C$_{10}$H$_8$N$_2$)I]$_4$(NO$_3$)$_8$, we investigate the ground-state properties of a Peierls-Hubbard four-legged tube. Making a group-theoretical analysis, we systematically reveal a variety of valence arrangements, including half-metallic charge-density-wave states. Quantum and thermal phase competition is numerically demonstrated with particular emphasis on doping-induced successive insulator-to-metal transitions with conductivity increasing stepwise.