The Interplay of Charge and Spin in Quantum Dots: The Ising Case

TL;DR

This paper investigates how charge and Ising-type spin interactions influence quantum dot behavior, providing analytical results for tunneling density of states and magnetic susceptibility that could guide experimental measurements.

Contribution

It introduces an Abelian model for charge and Ising spin interactions in quantum dots, simplifying the analysis of charge-spin entanglement compared to non-Abelian cases.

Findings

Calculated tunneling density of states

Analyzed dynamic magnetic susceptibility

Results accessible to experimental verification

Abstract

The physics of quantum dots is succinctly depicted by the {\it Universal Hamiltonian}, where only zero mode interactions are included. In the case where the latter involve charging and isotropic spin-exchange terms, this would lead to a non-Abelian action. Here we address an Ising spin-exchange interaction, which leads to an Abelian action. The analysis of this simplified yet non-trivial model shed some light on a more general case of charge and spin entanglement. We present a calculation of the tunneling density of states and of the dynamic magnetic susceptibility. Our results are amenable to experimental study and may allow for an experimental determination of the exchange interaction strength.