Exact ground states for pentagon chains with spin–orbit interaction

Exact ground states (GS) are deduced for conducting polymers possessing pentagon type of unit cell. The study is done in the presence of many-body spin–orbit interaction (SOI), local and nearest-neighbor Coulomb repulsion (CR), and presence of external E electric and B magnetic fields (EF). The simultaneous presence of SOI, CR, and EF in the exact conducting polymer GS is a novelty, so the development of the technique for the treatment possibility of such strongly correlated cases is presented in detail. The deduced GS show a broad spectrum of physical characteristics ranging from charge density waves doubling the system periodicity, metal–insulator transitions, to interesting external field-driven effects as, e.g., modification possibility of a static charge distribution by a static EF. Graphic abstract