Quantum rings for beginners II: Bosons versus fermions

TL;DR

This overview compares bosonic and fermionic systems in one-dimensional quantum rings, highlighting their differences in spectra and properties across various models, with relevance to recent experimental advancements.

Contribution

It provides a comprehensive comparison of boson and fermion quantum rings in 1D and Q1D regimes, emphasizing exact solutions for small systems.

Findings

Differences in many-body spectra between bosons and fermions.

Impact of interaction strength and spin on system properties.

Relevance to experimental fabrication of quantum rings.

Abstract

The purpose of this overview article, which can be viewed as a supplement to our previous review on quantum rings, [S. Viefers {\it et al}, Physica E {\bf 21} (2004), 1-35], is to highlight the differences of boson and fermion systems in one-dimensional (1D) and quasi-one-dimensional (Q1D) quantum rings. In particular this involves comparing their many-body spectra and other properties, in various regimes and models, including spinless and spinful particles, finite versus infinite interaction, and continuum versus lattice models. Our aim is to present the topic in a comprehensive way, focusing on small systems where the many-body problem can be solved exactly. Mapping out the similarities and differences between the bosonic and fermionic cases is of renewed interest due to the experimental developments in recent years, allowing for more controlled fabrication of both fermionic and bosonic quantum rings.