Synthetic Helical Liquids with Ultracold Atoms in Optical Lattices

TL;DR

This paper proposes a method to realize helical Tomonaga Luttinger liquids using ultracold fermionic atoms in optical lattices, combining analytical and numerical techniques to demonstrate its properties and robustness.

Contribution

It introduces a novel Fermi-Hubbard model at quarter filling that mimics HTLL behavior and provides a feasible experimental scheme for realization with ultracold atoms.

Findings

The model exhibits properties of helical Tomonaga Luttinger liquids.

Numerical and analytical methods confirm the long-wavelength behavior.

The system shows robustness against back-scattering and imperfections.

Abstract

We discuss a platform for the synthetic realization of key physical properties of helical Tomonaga Luttinger liquids (HTLLs) with ultracold fermionic atoms in one-dimensional optical lattices. The HTLL is a strongly correlated metallic state where spin polarization and propagation direction of the itinerant particles are locked to each other. We propose an unconventional one-dimensional Fermi-Hubbard model which, at quarter filling, resembles the HTLL in the long wavelength limit, as we demonstrate with a combination of analytical (bosonization) and numerical (density matrix renormalization group) methods. An experimentally feasible scheme is provided for the realization of this model with ultracold fermionic atoms in optical lattices. Finally, we discuss how the robustness of the HTLL against back-scattering and imperfections, well known from its realization at the edge of two-dimensional topological insulators, is reflected in the synthetic one-dimensional scenario proposed here.