Quantum Monte Carlo study of quantized muon in molecular systems

In muon spin relaxation/rotation/resonance $(\ensuremath{\mu}\mathrm{SR})$ technology, positive muons serve as local spin probes for detecting electron-muon or nucleus-muon spin interactions. Given that a muon's mass is approximately one-ninth that of a proton, its zero-point energy significantly influences $\ensuremath{\mu}\mathrm{SR}$ experiments. The straightforward application of the Born-Oppenheimer approximation fails to adequately address the muon's behavior from an ab initio perspective. Despite previous efforts to correct for the quantum effects of the muon, existing approximations often fall short, yielding unsatisfactory results. This paper addresses these limitations by focusing on the many-body system of quantized muons in materials and directly solving the muon-included many-body equation using quantum Monte Carlo techniques. We further simulate the hyperfine couplings of the muon, demonstrating that this rigorous approach can produce accurate results and explicit error margins. This method proves beneficial for $\ensuremath{\mu}\mathrm{SR}$ experiment analysis and holds potential for broader application in studying the quantum effects of heavy, positively charged particles in various materials.