Flat bands and Wigner crystallization in the honeycomb optical lattice

TL;DR

This paper investigates the ground states of cold atoms in a honeycomb optical lattice with flat bands, revealing crystalline order and dimerization phenomena at specific densities, and proposes experimental detection methods.

Contribution

It provides exact many-body ground states for flat band systems with on-site repulsion, highlighting novel crystalline and dimerized phases in a honeycomb lattice.

Findings

Crystalline order at particle density 1/6 with a $\,\sqrt{3} \times \sqrt{3}$ structure.

Dimerization of bonding strength at density 1/2 under strong repulsion.

Experimental detection via noise correlations in time-of-flight experiments.

Abstract

We study the ground states of cold atoms in the tight-binding bands built from p-orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at n=1/6 with a $\sqrt{3} \times \sqrt{3}$ structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes \emph{dimerized} at n=1/2. Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments.