Localization in One-Dimensional Interacting Electron Systems

Abstract

Recently it has been reported that low dimensional conductors are very sensitive to nonmagnetic impurities. Since this phenomenon may be related to the localization in low dimension, 1 we examine, for the first step, one-dimensional (1-D) electron systems in the presence of both impurities and mutual interactions. A competition between randomness and order arises because the impurity in the absence of interactions always leads to the localization2 and the interaction in the clean system results in the divergence of various kinds of response function.3 However both of these quantities cannot be treated by use of the usual perturbational method due to 1-D properties. There are two kinds of methods for studying the boundary between the delocalized state and the localized state in the plane of the coupling constant of the mutual interaction. One of them is the approach from the delocalized regime: the effect of impurities is examined by taking the clean system as an unperturbed state.4–6 Another of them is the approach from the localized regime: the localization is regarded as the impurity pinning of the phase variable of charge density wave (CDW).7, 8