# Ab Initio Exact Diagonalization Simulation of the Nagaoka Transition in Quantum Dots

## TL;DR

This paper introduces an ab initio exact diagonalization method to model correlated electrons in quantum dots, accurately studying the Nagaoka transition and ferromagnetism, aligning well with experimental data and advancing quantum simulator analysis.

## Contribution

The work presents a novel ab initio exact diagonalization framework that includes realistic multi-orbital effects to analyze ferromagnetism and the Nagaoka transition in quantum dots.

## Key findings

- Good agreement with experimental measurements of magnetism.
- Robustness of ferromagnetic states under various conditions.
- Insights into multi-orbital effects on the Nagaoka transition.

## Abstract

Recent progress of quantum simulators provides insight into the fundamental problems of strongly correlated systems. To adequately assess the accuracy of these simulators, the precise modeling of the many-body physics, with accurate model parameters, is crucially important. In this paper, we introduce an \emph{ab intio} exact diagonalization framework to compute the correlated physics of a few electrons in artificial potentials. We apply this approach to a quantum-dot system and study the magnetism of the correlated electrons, obtaining good agreement with recent experimental measurements. Through dot separation, potential detuning and control of single tunneling, we examine the Nagaoka transition and determine the robustness of the ferromagnetic state. While the standard Nagaoka theorem considers only a single-band Hubbard model, in this work we perform extensive $ab$ $intio$ calculations that include realistic multi-orbital conditions in which the level splitting is smaller than the interactions. This simulation complements the experiments and provides insight into the formation of ferromagnetism in correlated systems. More generally, our calculation sets the stage for further theoretical analysis of analog quantum simulators at a quantitative level.