Topological self-organization of strongly interacting particles

TL;DR

This paper explores how strongly interacting particles in 1D and 2D self-organize into many-body states with topological features, characterized by a topological number related to their real-space organization.

Contribution

It introduces a novel framework for identifying topological states in strongly interacting particles using real-space topology and provides analytical formulas for their energy spectrum and topological invariants.

Findings

Topological many-body states emerge at different energy bands.

The Euler characteristic serves as a topological number to classify states.

Analytical formulas for energy spectra and topological invariants are derived.

Abstract

We investigate the self-organization of strongly interacting particles confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice models with short-range interactions. We show that many-body states with topological features emerge at different energy bands separated by large gaps. The topology manifests in the way the particles organize in real space to form states with different energy. Each of these states contains topological defects/condensations whose Euler characteristic can be used as a topological number to categorize states belonging to the same energy band. We provide analytical formulas for this topological number and the full energy spectrum of the system for both sparsely and densely filled systems. Furthermore, we analyze the connection with the Gauss-Bonnet theorem of differential geometry, by using the curvature generated in real space by the particle structures. Our result is a demonstration of how states with topological characteristics, emerge in strongly interacting many-body systems following simple underlying rules, without considering the spin, long-range microscopic interactions, or external fields.