An exact scaling result for one dimensional interacting electronic systems

Abstract

For the one dimensional interacting electron system without umklapp processes, Sólyom has shown that to third order in the invariant charges, the Renormalization Group equations predict that g 1 − 2 g 2 is constant under scaling. We show that for g 1 − 2 g 2 = 0 this result is exact even in the strong coupling regime. The possible invariance of g 1 − 2 g 2 ≠ 0 is discussed.