Classification and stability of phases of the multicomponent one-dimensional electron gas

The classification of the ground-state phases of complex one-dimensional el ectronic systems is considered in the context of a fixed-point strategy. Ex amples are multichain Hubbard models, the Kondo-Heisenberg model, and the o ne-dimensional electron gas in an active environment.;It is shown that, in order to characterize the low-energy physics, it is necessary to analyze th e perturbative stability of the possible fixed paints, to identify all disc rete broken symmetries; and to specify the quantum numbers and elementary w ave vectors of the gapless excitations. Many previously proposed exotic pha ses of multichain Hubbard models are shown to be unstable because of the "s pin-gap proximity effect." A useful tool in this analysis is a generalizati on of Luttinger's theorem, which shows that there is a gapless even-charge mode, in any incommensurate N-component system. [S0163-1829(99)03124-0].