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Abstract

Luttinger liquids (LLs) are one-dimensional systems with well-understood instabilities due to Umklapp or backscattering. We study a generalization of the Luttinger model, which incorporates a time reversal symmetry breaking interaction producing a complex forward scattering amplitude (g(2) process). The resulting low energy state is still a LL and belongs to the family of interacting Schulz-Shastry models. Remarkably, it becomes increasingly robust against additional perturbations-for purely imaginary g(2), both Umklapp and local backscattering are always irrelevant. Changing the phase of the interaction generates a nontrivial Berry phase, with a universal geometric phase difference between ground and a one boson excited state depending only on the LL parameter.