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 ($\mathrm{C_{3}H_{8}O_{2}}$). By mapping the Stark-dressed rotational states onto an effective spin-$1/2$ subspace, we rigorously derive a generalized $XXZ$ 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 \textit{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~\mathrm{nm} ) and intermediate electric-field strengths ( d\varepsilon/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.

💡 Research Summary

The authors present a comprehensive proposal for realizing a quantum simulator of chiral quantum magnetism using linear arrays of trapped asymmetric‑top molecules, specifically 1,2‑propanediol (C₃H₈O₂). By applying a static electric field, the Stark‑dressed rotational spectrum of each molecule is engineered such that two low‑lying states—|J = 0, M = 0⟩ and |J = 1, K = −1, M = ±1⟩—form an effective spin‑½ subspace. The electric field mixes additional rotational components, but the chosen pair remains well isolated for a wide range of field strengths.

The total Hamiltonian consists of three parts: (i) the rigid‑rotor kinetic term with rotational constants A = 8572 MHz, B = 3640 MHz, C = 2790 MHz; (ii) the Stark interaction −d·ε, where the permanent dipole components are (dₐ = 1.201 D, d_b = 1.916 D, d_c = ±0.365 D) and ε is oriented along the laboratory z‑axis; and (iii) the dipole‑dipole interaction between neighboring molecules, expressed in spherical‑tensor form. By projecting the dipole‑dipole operator onto the spin‑½ basis, the authors derive an effective generalized XXZ Heisenberg Hamiltonian with an additional antisymmetric exchange term:

H_eff = ∑_i