Entangled and delocalized states of muons and nuclei

One of the central problems in physics, chemistry, and material science is finding accurate ab initio descriptions of properties of materials, which are ultimately made up of quantum electrons and nuclei, and quantum particles like muons, which are used to study them. The latter are produced in particle accelerators and implanted in materials as uniquely sensitive local probes of a material’s magnetism in the powerful experimental technique of muon spectroscopy (μSR), which can discern exceptionally small internal fields and their dynamics. However, the interpretation of μSR data can often be ambiguous due to unaccounted-for quantum effects of muons, including quantum uncertainty in their positions, quantum entanglement with nearby nuclear positions or spins, and quantum tunneling events. Because μSR is one of the few techniques that can be used to study spin dynamics in advanced quantum and topological materials, from superconductors and quantum spin liquids (QSL’s; materials in an unconventional, highly-entangled and dynamical spin state with proposed applications in robust topological quantum computing) to materials hosting skyrmions (vortices in magnetization protected against unwinding by their non-trivial topology), understanding quantum effects of muons is crucial. Similarly, quantum positional uncertainty and tunneling of light nuclei, which are effects that are usually missing in ab initio descriptions of nuclei, are known to strongly affect the structure and dynamics of important classes of advanced materials, including hydrogen-storage materials, materials with Li ions, and record high-Tc hydride superconductors. Powerful numerical methods like density functional theory (DFT) have proven extremely successful in describing the quantum behavior of electrons in a computationally-efficient way, unlocking a plethora of applications from understanding and predicting material properties to ab initio design of new materials. However, accurate, yet computationally-feasible, descriptions of the quantum behavior of muons and (light) nuclei in materials have largely remained elusive. Their quantum effects are thus often unjustly neglected and they are instead described as classical, point particles. However, in modern ab initio calculations the unaccounted-for quantum effects of nuclei are often the dominant source of inaccuracy, that is, discrepancy between predictions of calculations and experiment. Quantum effects of muons are even more pronounced, as muons are approximately nine-times lighter than even the lightest nucleus — a lone proton — which makes them even more challenging to describe. Progress in ab initio descriptions of muons and nuclei is therefore key for advancing the fields of condensed matter physics and chemistry. This project will develop the necessary theoretical tools and numerical methods to efficiently describe quantum effects of muons and light nuclei, and apply them to the study of both: (i) paradigmatic materials where muons and nuclei particularly clearly exhibit certain types of quantum behavior, as well as (ii) QSL materials with intriguing quantum spin and impurity dynamics, where quantum effects of muons are crucial for the correct interpretation of μSR data. Our approach will be based on our recent breakthrough, proof-of-concept study of muons implanted in solid nitrogen, where we were able, for the first time, to identify key entanglement and anharmonicity parameters that determine a muon’s quantum regime in a material. We will extend this pioneering study to a practical approach for treating quantum effects of arbitrary light particles (muons or nuclei) in a lattice of heavier nuclei. This project will thus unlock the full potential of the powerful μSR technique in the study of advanced materials, and finally enable reliable ab initio prediction and understanding of crucial quantum effects of muons and nuclei in a wide range of quantum materials.