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 ( C 3 H 8 O 2 ). By mapping the Stark-dressed rotational states onto an effective spin- 1 / 2 subspace, we rigorously derive a generalized X X Z 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 from the molecular stereochemistry. Specifically, the interference between the transition dipole moments of heterochiral enantiomer pairs (left- and right-handed), 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 ≈ 1.5 nm and intermediate electric-field strengths d ɛ / B ≈ 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.