Generic Hubbard model description of semiconductor quantum dot spin qubits

TL;DR

This paper presents a Hubbard model for semiconductor quantum-dot spin qubits that incorporates quantum effects like hopping and spin exchange, providing a quantitative link to experimental data and revealing quantum details in stability diagrams.

Contribution

The authors develop a Hubbard model that extends classical capacitance models to include quantum effects, enabling direct extraction of quantum information from experimental stability diagrams.

Findings

Hubbard model reproduces classical capacitance results without quantum fluctuations.

Quantum effects influence fine details of charge stability diagrams.

Model parameters can be derived from experiments or microscopic theory.

Abstract

We introduce a Hubbard model as the simple quantum generalization of the classical capacitance circuit model to study semiconductor quantum-dot spin qubits. We prove theoretically that our model is equivalent to the usual capacitance circuit model in the absence of quantum fluctuations. However, our model naturally includes quantum effects such as hopping and spin exchange. The parameters of the generalized Hubbard model can either be directly read off from the experimental plot of the stability diagram or be calculated from the microscopic theory, establishing a quantitative connection between the two. We show that, while the main topology of the charge stability diagram is determined by the ratio between inter-site and on-site Coulomb repulsion, fine details of the stability diagram reveal information about quantum effects. Extracting quantum information from experiments using our Hubbard model approach is simple, but would require the measurement resolution to increase by an order of magnitude.