Spectrum and Screening cloud in the central spin model

TL;DR

This paper investigates the spectral and correlation properties of an electron spin in a quantum dot coupled to nuclear spins, using the exact Bethe Ansatz solution of the Gaudin's central spin model, revealing classical and quantum contributions.

Contribution

It provides a detailed analysis of the nuclear spin screening cloud and links it to the BCS model, distinguishing classical and quantum effects in the central spin system.

Findings

Characterization of the nuclear spin screening cloud structure.

Connection established between the central spin model and BCS pair occupation.

Identification of classical versus quantum contributions in the model.

Abstract

We consider an electronic spin in a quantum dot, coupled to the surrounding nuclear spins via inhomogeneous antiferromagnetic hyperfine interactions and subject to a uniform field, which is described by Gaudin's central spin model. We study spectral properties, the two-point correlation functions, and the magnetization profile in the ground state and in low-lying excited states, which characterizes the structure of the cloud of nuclear spins screening the electron spin. A close connection to the pair occupation probability in the BCS-model is established. Using the exact Bethe Ansatz solution of that model and arguments of integrability, we can distinguish between contributions from purely classical physics and from quantum fluctuations.