Possible Phases and Some Properties of the One-Dimensional Metal with the Half-Filled Band

Abstract

A one-dimensional metal with a half-filled band is studied by the model of Dzyaloshinskii and Larkin. The next-order renormalization group theory is applied. The invariant charges become smooth functions over all temperature. The possible phases–the singlet and the triplet Cooper pairing states, and SDW and CDW at T →0 are discussed. The criterion for these phases depends on the bare coupling constants via their signs and relative magnitudes. The phase diagram differs from that of the first-order theory. The Green's function, the vertex function, and 2p_F and uniform response functions are found in the asymptotic power form. The exponents are universal except for the case of the repulsive couplings. The results are compared with the exact theorems about the Hubbard and Tomonaga models.