  We study a twisted Hubbard tube modeling the [CrAs] structure of
quasi-one-dimensional superconductors A2Cr3As3 (A = K, Rb, Cs). The
molecular-orbital bands emerging from the quasi-degenerate atomic orbitals are
exactly solved. An effective Hamiltonian is derived for a region where three
partially filled bands intersect the Fermi energy. The deduced local
interactions among these active bands show a significant reduction compared to
the original atomic interactions. The resulting three-channel Luttinger liquid
shows various interaction-induced instabilities including two kinds of
spin-triplet superconducting instabilities due to gapless spin excitations,
with one of them being superseded by the spin-density-wave phase in the
intermediate Hund's coupling regime. The implications of these results for the
alkali chromium arsenides are discussed.
