We consider the problem of including \(\varLambda \) 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.

我们考虑包括\（\ varLambda \）的问题超子进入核晶格有效场论的从头算框架。为了避免蒙特卡洛模拟中的大符号振荡，我们利用以下事实：与感兴趣的超核中的核子数量相比，超子的数量通常较小。这使我们可以使用杂质晶格蒙特卡罗方法，其中完整核哈密顿量中的少数费米子物种被整合出来，并作为欧几里得投影时间的世界线。大多数的费米子（核子）被视为明确的自由度，它们的相互作用由辅助场描述。这是杂质晶格蒙特卡罗方法在多数粒子相互作用的系统上的首次应用。这里，我们展示了如何将杂质蒙特卡洛方法应用于计算光超核的结合能。在这项探索性工作中，我们使用自旋无关的核子-核子和超子-核子相互作用来测试该方法的计算能力。我们发现计算工作量在核子数量上近似线性缩放。该结果对于使用手性有效场理论和现实的超子-核子相互作用以及对其他量子多体系统的应用对大型超核系统的未来研究而言，是非常有希望的。