  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 non-trivial Berry phase, with a universal geometric
phase difference between ground and a one boson excited state depending only on
the LL parameter.
