Emergence of a Luttinger Liquid Phase in an Array of Chiral Molecules

We propose a robust platform for simulating chiral quantum magnetism using linear arrays of trapped asymmetric top molecules, specifically 1,2-propanediol $mathrm{C₃H₈O₂}$. By mapping the Stark-dressed rotational states onto an effective spin-1/2 subspace, we rigorously derive a generalized XXZ Heisenberg Hamiltonian governing the underlying many-body dynamics. Unlike standard solid-state models where the topological Dzyaloshinskii-Moriya Interaction (DMI) is introduced phenomenologically, we demonstrate that DMI emerges ab initio from the molecular stereochemistry. Specifically, the interference between the transition dipole moments of heterochiral enantiomer pairs (L-R), which breaks inversion symmetry, generates a tunable DMI that stabilizes a Chiral Luttinger Liquid phase. Through a comprehensive phase-diagram analysis, we identify an optimal experimental regime characterized by intermolecular separations of r approx 1.5 nm and intermediate electric-field strengths dvarepsilon/B approx 2.5. In this window, the system is protected from trivial field-polarized phases and exhibits a robust gapless spin-spiral texture. Our results establish 1,2-propanediol arrays as a versatile quantum simulator, providing a direct microscopic link between molecular chirality and topological many-body phases.