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

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Abstract
We show that a large class of backward-scattering matrix elements involving Δk ∼ ± 2kF 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.

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