Aliphatic Chains as One-Dimensional XY Spin Chains

TL;DR

This paper demonstrates that aliphatic chains in liquid-state NMR can behave as one-dimensional XY spin chains, enabling the study of spin wave dynamics and many-body quantum phenomena in molecular systems.

Contribution

It introduces a novel analogy between aliphatic chain NMR and the XY spin model, providing analytical solutions and identifying molecular systems suitable for quantum simulation.

Findings

Spin waves propagate in liquid-state NMR of aliphatic chains.

The spin Hamiltonian factorizes into XY model subspaces.

Potential for quantum simulation of complex spin dynamics.

Abstract

Spin waves are propagating disturbances of spin order in lattices with nearest-neighbor interactions. They are traditionally observed in magnetically ordered solids using inelastic neutron, light, or electron scattering, and ferromagnetic resonance. Here, we show that analogous spin dynamics can arise in liquid-state nuclear magnetic resonance (NMR) of molecules containing aliphatic chains. In such molecules, each CH_2 group must have a distinct chemical shift and be magnetically inequivalent via out-of-pair couplings. Under these conditions, singlet state populations of geminal protons propagate along (CH_2)_n segments forming magnetically silent spin waves. For a chain with translational symmetry, the spin Hamiltonian factorizes into subspaces formally equivalent to the one-dimensional XY model. This correspondence yields analytic expressions for eigenstates and eigenenergies in a spectroscopy we term spin-chain zero-quantum NMR. We identify molecular systems in which these conditions are met. Their collective dynamics rapidly exceed classical computational tractability, making them targets for quantum-computer simulations of spin transport and many-body dynamics.