Impurity lattice Monte Carlo for hypernuclei

We consider the problem of including Λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda $$\end{document} hyperons into the ab initio framework of nuclear lattice effective field theory. In order to avoid large sign oscillations in Monte Carlo simulations, we make use of the fact that the number of hyperons is typically small compared to the number of nucleons in the hypernuclei of interest. This allows us to use the impurity lattice Monte Carlo method, where the minority species of fermions in the full nuclear Hamiltonian is integrated out and treated as a worldline in Euclidean projection time. The majority fermions (nucleons) are treated as explicit degrees of freedom, with their mutual interactions described by auxiliary fields. This is the first application of the impurity lattice Monte Carlo method to systems where the majority particles are interacting. Here, we show how the impurity Monte Carlo method can be applied to compute the binding energies of the light hypernuclei. In this exploratory work we use spin-independent nucleon–nucleon and hyperon–nucleon interactions to test the computational power of the method. We find that the computational effort scales approximately linearly in the number of nucleons. The results are very promising for future studies of larger hypernuclear systems using chiral effective field theory and realistic hyperon–nucleon interactions, as well as applications to other quantum many-body systems.