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Based on a positive semidefinite operator technique, exact ground states arededuced for the non-integrable conducting polymers possessing pentagon type ofunit cell. The study is done in the presence of many-body spin-orbitinteraction (SOI), local and nearest neighbor Coulomb repulsion (NNCR) andpresence of external $E$ electric and $B$ magnetic fields, such that theeffects of $B$ on both orbital and spin degrees of freedom is considered. TheSOI, NNCR, and presented external field configurations presence in exactconducting polymer ground states is a novelty, so the development of thetechnique for the treatment possibility of such strongly correlated cases ispresented in details. The deduced ground states show a broad spectrum ofphysical characteristics ranging from charge density waves, metal-insulatortransitions, to interesting external field driven effects as e.g. modificationpossibility of a static charge distribution by a static external magneticfield.

Pentagon chain with spin orbit interactions: exact many-body ground states in the interacting case