The electronic spin in quantum dots can be described by central spin models (CSMs) with a very large number Neff≈104 to 106 of bath spins posing a tremendous challenge to theoretical simulations. Here, a fully quantum mechanical theory is developed for the limit Neff→∞ by means of iterated equations of motion (iEoM). We find that the CSM can be mapped to a four-dimensional impurity coupled to a non-interacting 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 is tested successfully against data from other, established approaches. Thus, the iEoM mapping extends the set of theoretical tools which can be used to understand the spin dynamics in large CSMs.
@article{arxiv.1711.08919,
title = {Quantum mechanical treatment of large spin baths},
author = {Robin Röhrig and Philipp Schering and Lars B. Gravert and Benedikt Fauseweh and Götz S. Uhrig},
journal= {arXiv preprint arXiv:1711.08919},
year = {2018}
}