Many-body quantum muon effects and quadrupolar coupling in solids

Strong quantum zero-point motion (ZPM) of light nuclei and other particles is a crucial aspect of many state-of-the-art quantum materials. However, it has only recently begun to be explored from an ab initio perspective, through several competing approximations. Here we develop a unified description of muon and light nucleus ZPM and establish the regimes of anharmonicity and positional quantum entanglement where different approximation schemes apply. Via density functional theory and path-integral molecular dynamics simulations we demonstrate that in solid nitrogen, alpha-N-2, muon ZPM is both strongly anharmonic and many-body in character, with the muon forming an extended electric-dipole polaron around a central, quantum-entangled [N-2-mu-N-2](+) complex. By combining this quantitative description of quantum muon ZPM with precision muon quadrupolar level-crossing resonance experiments, we independently determine the static N-14 nuclear quadrupolar coupling constant of pristine alpha-N-2 to be -5.36(2) MHz, a significant improvement in accuracy over the previously-accepted value of -5.39(5) MHz, and a validation of our unified description of light-particle ZPM. Quantum entanglement and uncertainty in the positions of light nuclei and implanted particles can crucially impact our understanding of advanced materials. This paper develops a unified theoretical description of these effects and applies it to muon spectroscopy measurements of a material constant to significantly improve their accuracy.