Ferromagnetic--nematic order and strongly correlated phases of fermions in optical flux lattices

TL;DR

This paper investigates a 2D ultracold fermionic gas in an optical flux lattice, revealing ferromagnetic--nematic order, a Laughlin-like fractional quantum Hall state at 1/3 filling, and a charge density wave at 1/2 filling through exact diagonalization.

Contribution

It provides the first detailed numerical evidence for ferromagnetic--nematic order and fractional quantum Hall states in a realistic optical flux lattice model.

Findings

Evidence for ferromagnetic--nematic order at certain fillings.

Identification of a Laughlin-like fractional quantum Hall state at ν=1/3.

Observation of a charge density wave state at ν=1/2.

Abstract

We study a model of a 2D ultracold atomic gas subject to an "optical flux lattice": a laser configuration where Raman-dressed atoms experience a strong artificial magnetic field. This leads to a bandstructure of narrow energy bands with non-zero Chern numbers. We consider the case of two-level (spin-$1/2$) fermionic atoms in this lattice, interacting via a repulsive $s$-wave contact interaction. Atoms restricted to the lowest band are described by an effective model of spinless fermions with interactions that couple states in a momentum-dependent manner across the Brillouin zone; a consequence of the Raman dressing of the two spin states. We present the results of detailed exact diagonalization studies of the many-body states for a range of filling factors, $\nu$. First, we present evidence for the existence of a phase with coupled ferromagnetic--nematic ordering, which was previously suggested by a mean-field analysis. Second, we present evidence indicating the presence of a Laughlin-like fractional quantum Hall state occurring at filling factor $\nu = 1/3$. Finally, we observe a charge density wave state at $\nu=1/2$, which we are able to cleanly distinguish from the Laughlin-like state by its translational symmetry breaking and relatively small participation ratio.