Quantum mechanical treatment of large spin baths

The electronic spin in quantum dots can be described by central spin models (CSMs) with a very large number ${N}_{\text{eff}}\ensuremath{\approx}{10}⁴$ to ${10}⁶$ of bath spins posing a tremendous challenge to theoretical simulations. Here, a fully quantum mechanical theory is developed for the limit ${N}_{\text{eff}}\ensuremath{\rightarrow}\ensuremath{\infty}$ by means of iterated equations of motion (iEoM). We find that the CSM can be mapped to a four-dimensional impurity coupled to a noninteracting bosonic bath in this limit. Remarkably, even for infinite bath the CSM does not become completely classical. The data obtained by the proposed iEoM approach are tested successfully against data from other, established approaches. Thus the iEoM mapping extends the set of theoretical tools that can be used to understand the spin dynamics in large CSMs.