New wave-operator identity applied to the study of persistent currents in 1D

Abstract

We show that a large class of backward‐scattering matrix elements involving Δk ∼ ± 2k_F vanish for fermions interacting with two‐body attractive forces in one dimension. (These same matrix elements are finite for noninteracting particles and infinite for particles interacting with two‐body repulsive forces.) Our results demonstrate the possibility of persistent currents in one dimension at T = 0, and are a strong indication of a metal‐to‐insulator transition at T = 0 for repulsive forces. They are obtained by use of a convenient representation of the wave operator in terms of density‐fluctuation operators.