Two coupled chains with Tomonaga-Luttinger interactions

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Abstract
We analyze the infrared asymptotic properties of two chains coupled by one-electron tunneling, when electron interactions are restricted to a small momentum transfer. We study two different situations. In the presence of interactions between oppositely moving particles, the strong-coupling regime develops. We show that eventually two coupled modes, describing the internal dynamics of the chains, acquire gaps in their spectra, independent of the sign of the bare interaction. When the interaction is retained only for particles moving in the same direction, the infrared properties are determined by four decoupled gapless modes. However, the propagation of one of them, due to the peculiar form of the nonlinear interactions, exhibits nonquasiparticle features. We obtain the asymptotic form of the one-particle Green function in this case. The analysis carried out can be useful for the description of edge states in a two-dimensional system under the quantum Hall-effect conditions.