Luttinger liquid with complex forward scattering: robustness and Berry phase

TL;DR

This paper explores a generalized Luttinger liquid model with complex forward scattering, revealing enhanced robustness against perturbations and uncovering a universal Berry phase related to the interaction's phase.

Contribution

It introduces a Luttinger model with complex forward scattering that remains stable under perturbations and exhibits a universal Berry phase depending on the LL parameter.

Findings

Purely imaginary $g_2$ makes umklapp and backscattering irrelevant.

The model's ground state is a robust LL with complex interactions.

A universal geometric Berry phase depends only on the LL parameter.

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