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We study the quantum self-organization of interacting particles inone-dimensional(1D) many-body systems, modeled via Hubbard chains withshort-range interactions between the particles. We show the emergence of 1Dstates with density-wave and clustering order, related to topology, at odddenominator fillings that appear also in the fractional-quantum-Hall-effect(FQHE), which is a 2D electronic system with Coulomb interactions between theelectrons and a perpendicular magnetic field. For our analysis we use aneffective topological measure applied on the real space wavefunction of thesystem, the Euler characteristic describing the clustering of the interactingparticles. The source of the observed effect is the spatial constraints imposedby the interaction between the particles. In overall, we demonstrate a simplemechanism to reproduce many of the effects appearing in the FQHE, withoutrequiring a Coulomb interaction between the particles or the application of anexternal magnetic field.

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