Regular Article - Solid State and Materials
Fractional-quantum-Hall-effect (FQHE) in 1D Hubbard models
1 Physics Division, National Center for Theoretical Sciences, 30013, Hsinchu, Taiwan
2 Department of Physics, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel
Accepted: 8 January 2021
Published online: 1 February 2021
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.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021