Quantum mechanical treatment of large spin baths

TL;DR

This paper develops a quantum mechanical theory for large central spin models in quantum dots, mapping them to a four-dimensional impurity problem and providing a new tool for understanding spin dynamics with very large baths.

Contribution

A fully quantum mechanical approach using iterated equations of motion is introduced for large spin baths, enabling analysis of systems with up to a million spins.

Findings

CSM maps to a four-dimensional impurity coupled to a bosonic bath

Even with infinite bath, the system retains quantum characteristics

The approach agrees well with established methods

Abstract

The electronic spin in quantum dots can be described by central spin models (CSMs) with a very large number $N_\mathrm{eff} \approx 10^4$ to $10^6$ of bath spins posing a tremendous challenge to theoretical simulations. Here, a fully quantum mechanical theory is developed for the limit $N_\mathrm{eff} \to \infty$ by means of iterated equations of motion (iEoM). We find that the CSM can be mapped to a four-dimensional impurity coupled to a 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.