Coexisting N\'eel and charge density wave orders in attractive three-color fermions

Abstract

In optical lattices attractive ultracold fermions with three hyperfine-spin components (colors) can form three fermionic configurations depending on interactions: unbound fermion, on-site trion and off-site trion, leading to the coexistence of multiple Fermi species in the ordered phase, which manifests that the attractive three-color fermions are unique from other correlated fermion systems and may host intriguing phases and phase transitions. At temperature below the superexchange energy scale, we employ the determinant quantum Monte Carlo (QMC) method to investigate the phases and phase transitions in the half-filled attractive three-color Hubbard model on a honeycomb lattice where Hubbard interactions are color-dependent (anisotropic interactions) and the coupling between color 3 and colors (1, 2) serves as a control parameter. In the coupling regime where on-site and off-site trions coexist, our QMC simulations demonstrate coexisting N\'eel and charge density wave orders which are common in condensed matter but rare in ultracold atoms. At weak coupling where the color superfluid (CSF) order is scattered by color-3 fermions, we find that very small coupling of color 3 with colors (1, 2) can destroy the CSF order and the vanishing of the CSF order is not immediately accompanied by the emergence of the on-site trionic phase, which strikingly disagrees with the prevalent results of dynamical mean-field theory. The underlying mechanisms of the coexisting charge/spin orders and the CSF order breaking are also presented based on intuitive physical pictures.