Wigner crystallization in topological flat bands

TL;DR

This paper investigates Wigner crystallization in topological flat bands, revealing how particle density and boundary conditions influence crystal formation, with results derived from exact diagonalization analysis.

Contribution

It provides a detailed analysis of Wigner crystal formation in topological flat bands, highlighting the roles of density and boundary conditions, and showing independence from lattice topology.

Findings

Crystallization strength increases as particle density decreases.

Wigner crystal shapes are mainly determined by boundary conditions.

Crystals behave similarly to classical point particles regardless of lattice topology.

Abstract

We study the Wigner crystallization on partially filled topological flat bands. We identify the Wigner crystals by analyzing the cartesian and angular Fourier transform of the pair correlation density of the many-body ground state obtained using exact diagonalization. The crystallization strength measured by the magnitude of the Fourier peaks, increases with decreasing particle density. The shape of the resulting Wigner crystals is determined by the boundary conditions of the chosen plaquette and to a large extent independent on the underlying lattice, including its topology, and follows the behavior of classical point particles.