A one-dimensional system of electrons with interaction parameters
g1 and
g2 is studied by applying the third-order renormalization-group technique. For
g1>0 our result is essentially the same as that obtained previously in the first-order scaling. For
g1<0 the invariant coupling $\frac{{{g}^{\ensuremath{'}}}_{1}}{\ensuremath{\pi}v}\ensuremath{\simeq}\ensuremath{-}0.87$ is considerably weaker than that $\frac{{{g}^{\ensuremath{'}}}_{1}}{\ensuremath{\pi}v}=\ensuremath{-}2$ in the second-order renormalization obtained by Menyh\'ard and S\'olyom in the low-frequency limit. The phases of the ground state in the present approximation are the same as those predicted in the second-order renormalization. The critical exponents for response functions which describe various critical fluctuations have also been calculated.
We analyze the spectral properties of a very general two-channel fermion-boson transport model in the insulating and metallic regimes and the signatures of the metal-insulator quantum phase transition in between. To this end we determine the single-particle spectral function related to angle-resolved photoemission spectroscopy, the momentum distribution function, the Drude weight, and the optical response by means of a dynamical (pseudosite) density-matrix renormalization group technique for the one-dimensional half-filled band case. We show how the interplay of correlations and fluctuations in the background medium controls the charge dynamics of the system, which is a fundamental problem in a great variety of advanced materials.