Application of the Mean-Field Approximation to the Magnetic and Superconducting Phases of Quasi-One-Dimensional Metal

We research under what condition the mean-field approximation can be applied to study ordered phases of quasi-one-dimensional metal. It is shown that the mean-field treatment is indeed permissible provided that it is applied not to the microscopic Hamiltonian (subject to severe one-dimensional high-energy fluctuations), but rather to effective Hamiltonian derived at the dimensional crossover scale. The resultant mean-field phase diagram has three ordered phases: spin density wave, charge density wave, and superconductivity. The density wave orders win if the Fermi surface nests well. Outcome of competition between the intra-chain and inter-chain electron repulsion determines the type (spin vs. charge) of the density wave. The ground state becomes superconducting (with unconventional order parameter) when the nesting is poor. The superconducting mechanism relies crucially on the one-dimensional fluctuations.