Monte Carlo study of fermionic trions in a square lattice with harmonic confinement

We investigate the strong-coupling limit of a three-component Fermimixture in an optical lattice with attractive interactions. In this limit bound states (trions) of the three components are formed. We study the effective Hamiltonian for these composite fermions and show that it is asymptotically equivalent at the leading order to an antiferromagnetic Ising model. By using Monte Carlo simulations, we investigate the spatial arrangement of the trions in this regime and the formation of a trionic density wave, both in a homogeneous lattice and in the presence of an additional harmonic confinement. Depending on the strength of the confinement and on the temperature, we found several scenarios for the trionic distribution, including the coexistence of disordered trions with a density wave and band insulator phases. Our results show that, due to a proximity effect, staggered density modulations are induced in regions of the trap where they would not otherwise be present according to the local density approximation.