1D Quantum Magnetism from Molecular Chirality: Emergence of Chiral Luttinger Liquids and Stereochemical Edge States

Ultracold molecular platforms are rapidly emerging as highly tunable environments for quantum simulation. In this talk, I will demonstrate how the intrinsic stereochemistry of chiral molecules can be harnessed to engineer complex topological and many-body quantum phases from the ground up.

First, I will explore the many-body dynamics of linear arrays of trapped asymmetric top molecules, specifically 1,2-propanediol. I will show how the Dzyaloshinskii-Moriya Interaction (DMI) emerges ab initio in these systems. We demonstrate that the interference between transition dipole moments of heterochiral enantiomer pairs generates a tunable DMI that stabilizes a robust Chiral Luttinger Liquid phase. Through a comprehensive phase-diagram analysis, we identify the optimal electric-field and spatial regimes to protect this gapless spin-spiral texture from trivial field-polarized phases.

Building on this chirality-induced DMI, I will then present a general theoretical framework for realizing topological edge states in dimerized arrays of chiral dipolar molecules. By mapping Stark-dressed chiral molecules to an effective spin-1/2 model, we show that the DMI naturally amplifies the effective hopping amplitudes and enlarges the bulk topological gap relative to an achiral chain. Most notably, this geometry produces in-gap boundary modes that carry opposite molecular chirality—a unique stereochemical labeling where the left edge state localizes on a left-handed molecule and the right edge state on a right-handed molecule.