The Emergence of the Noninteracting Channel in the Strongly Interacting 1D System

A strongly interacting 1D system with many channels is studied. When single-electron interchannel backscattering processes become relevant, new fields are defined. Some fields are frozen (gapped) by these relevant perturbations, whereas others remain free. A mathematical procedure to separate gapped and conducting channels is proposed. The problem for a two-channel system with particular relevant perturbation is then solved exactly for arbitrary intra- and interchannel interactions, and effective Luttinger parameter and velocity for the free field are found. The parameters of the free field are independent of the interactions between right- and left-moving electrons in the same channel and between electrons moving in the same direction in different channels. Finally, if the interchannel interactions are weak, the free field becomes noninteracting (effective Luttinger parameter Keff=1) independently of how strong intrachannel interactions are.