Interacting electrons in a magnetic field: mapping quantum mechanics to a classical ersatz-system

TL;DR

This paper explores how quantum many-electron problems in magnetic fields can be mapped onto classical systems, enabling more efficient simulations and offering insights into quantum-classical transitions.

Contribution

It introduces a novel mapping technique that translates quantum electron interactions in magnetic fields into classical dynamics for improved computational efficiency.

Findings

Mapping reduces computational complexity for many-body systems.

Provides a framework for simulating quantum phenomena classically.

Enhances understanding of quantum-to-classical transition in electronic systems.

Abstract

Solving the quantum-mechanical many-body problem requires scalable computational approaches, which are rooted in a good understanding of the physics of correlated electronic systems. Interacting electrons in a magnetic field display a huge variety of eigenstates with different internal structures, which have been probed experimentally in the Hall effect. The advent of high-performing graphics processing units has lead to a boost in computational speed in particular for classical systems. In the absence of a quantum-computer, it is thus of importance to see how quantum-mechanical problems can be cast into a seemingly classical dynamics, which can be efficiently implemented. At the same time, such mappings provide insights into the quantum-to-classical transition of many-body systems.