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

TL;DR

This work proposes a molecular quantum-simulation platform using linear arrays of chiral asymmetric-top molecules (1,2-propanediol) to realize chiral quantum magnetism. By mapping Stark-dressed rotational states onto an effective spin-1/2, it derives a generalized XXZ Hamiltonian in which a Dzyaloshinskii–Moriya interaction arises ab initio from molecular chirality and external fields. The authors compute the effective couplings (Jxy, Jz, D, h), map to a rotated XXZ model with tilde Jxy = sqrt(Jxy^2 + D^2), and identify an optimal parameter window at r ≈ 1.5 nm and dε/B ≈ 2.5 that supports a robust chiral Luttinger-liquid phase. The proposed experimental route via superfluid helium nanodroplets offers sub-nanometer control and a clean environment to observe algebraic spin correlations and chiral textures, with potential extensions to topological edge modes and domain-wall engineering. Overall, the work links molecular chirality to topological many-body phases and provides a versatile platform for exploring chiral quantum magnetism and CISS-related phenomena.

Abstract

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.

Figures (10)

• Figure 1: (a) Schematic representation of two rotating prolate asymmetric-top molecules (1,2-propanediol) with permanent electric dipole moments $\mathbf{d}_1$ and $\mathbf{d}_2$, interacting with an external dc electric field $\boldsymbol{\varepsilon}$. The laboratory-fixed reference frame $(X, Y, Z)$ is chosen such that the intermolecular separation vector satisfies $\mathbf{r}=r\,\mathbf{e}_Z$. Each molecule is associated with its own molecule-fixed frame $(x_i,y_i,z_i)$. Due to molecular chirality, the dipole moments $\mathbf{d}_i$ have opposite orientations with respect to their corresponding body-fixed frames for the two enantiomers.(b) Schematic representation of the total angular momentum $\mathbf{J}$ with respect to the laboratory-fixed axis $\mathbf{e}_Z$ and the molecule-fixed principal axis $\mathbf{e}_z$.
• Figure 2: Eigenenergies of the asymmetric-top molecule 1,2-propanediol $(\mathrm{C_{3}H_{8}O_{2}})$ in an external dc electric field, plotted as a function of $d\varepsilon/B$, where $d$ is the permanent dipole moment, $\varepsilon$ is the electric-field strength, and $B$ is the rotational constant. In the absence of the electric field, the states $\lvert j=0,k=0,m=0\rangle$ and $\lvert j=1,k=-1,m=\pm1\rangle$ are identified as the pseudo-spin states $\lvert\downarrow\rangle$ (solid red curve) and $\lvert\uparrow\rangle$(dotted blue curve), respectively.
• Figure 3: Field dependence of the expansion coefficients $c_{\tilde{j},\tilde{k}}(x=d\varepsilon/B)$ for the pseudo-spin states $\lvert\downarrow\rangle=\lvert\tilde{j},\tilde{k},m=0\rangle$ (left panel) and $\lvert\uparrow\rangle=\lvert\tilde{j},\tilde{k},m=\pm1\rangle$ (right panel); see Eq. \ref{['Eq3']}.
• Figure 4: Matrix elements of $C_{1}$, $C_{2}$, $C_{3}$, and $C_{4}$ as functions of the dimensionless electric-field interaction parameter $d\varepsilon/B$. The dotted green curves correspond to $C_{2}$ and $C_{3}$, which are equal in magnitude for the (1,2-propanediol) molecule configuration. In contrast, $C_{1}$ (solid red) and $C_{4}$ (solid blue) are initially distinct but gradually converge at larger field strengths.
• Figure 5: Imaginary parts of the dipolar coefficients $C_{d_1}$ and $C_{d_2}$ as functions of the electric-field parameter $d\varepsilon/B$. The two coefficients are equal in magnitude and opposite in sign ($C_{d_1} = -C_{d_2}$); this antisymmetry constitutes the microscopic origin of the effective Dzyaloshinskii--Moriya interaction, which causes neighboring spins to be slightly twisted relative to each other, rather than strictly parallel or antiparallel.