Fractional-quantum-Hall-effect (FQHE) in 1D Hubbard models

TL;DR

This paper demonstrates that fractional quantum Hall-like states can emerge in one-dimensional Hubbard models through particle interactions and topological measures, without the need for Coulomb interactions or magnetic fields.

Contribution

It introduces a novel mechanism showing FQHE-like phenomena in 1D systems using topological analysis, bypassing traditional 2D Coulomb and magnetic field requirements.

Findings

Emergence of density-wave and clustering order in 1D Hubbard chains.

Topological measure (Euler characteristic) reveals clustering related to FQHE.

FQHE-like effects reproduced without Coulomb interactions or magnetic fields.

Abstract

We study the quantum self-organization of interacting particles in one-dimensional(1D) many-body systems, modeled via Hubbard chains with short-range interactions between the particles. We show the emergence of 1D states with density-wave and clustering order, related to topology, at odd denominator fillings that appear also in the fractional-quantum-Hall-effect (FQHE), which is a 2D electronic system with Coulomb interactions between the electrons and a perpendicular magnetic field. For our analysis we use an effective topological measure applied on the real space wavefunction of the system, the Euler characteristic describing the clustering of the interacting particles. The source of the observed effect is the spatial constraints imposed by the interaction between the particles. In overall, we demonstrate a simple mechanism to reproduce many of the effects appearing in the FQHE, without requiring a Coulomb interaction between the particles or the application of an external magnetic field.