Abstract
Several exact results are proved for two models of one-dimensional conductors, a model with transfer cutoff and spin- and charge-carrying interactions and the usual backscattering model with a bandwidth cutoff. A set of Ward identities is derived which connects the three-point charge vertex parts with single-particle Green's functions. These are combined with a modified renormalization-group scheme to prove the scale invariance of the couplings between charge densities in the absence of umklapp processes. The Ward identities are also used for the computation of the correlation functions in the charge sector of the system. Then some canonical transformations are introduced which allow one to relate various response functions among themselves. From these relations the phase boundaries of the ground state can be established. It is shown that the transfer cutoff and the backscattering models have the same phase diagram.
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