Trion ordering in the attractive three-color Hubbard model on a $π$-flux square lattice

Abstract: Ultracold multicomponent fermions (atoms/molecules) loaded in optical lattices provide an ideal platform for simulating SU($N$) Hubbard models that host unconventional many-body quantum states beyond SU(2). A prime example is the attractive three-color Hubbard model, in which trion states emerge at strong coupling. Nevertheless, much of its trion ordering on two-dimensional lattices remains uncertain. Here, we employ the determinant quantum Monte Carlo (DQMC) method to simulate the attractive three-color Hubbard model on a $π$-flux square lattice at half filling. We show that color-dependent attractive interaction can induce coexisting charge density wave (CDW) and Néel ordered states in the three-color $π$-flux Hubbard model. In particular, enhanced charge fluctuations (cf. honeycomb lattice) cause much stronger Néel ordering on the $π$-flux square lattice. The coexisting charge and Néel orders survive up to a melting temperature, at which they vanish simultaneously. The Ginzburg-Landau (GL) analysis on the coexistence of CDW and Néel orders demonstrates how color-dependent Hubbard interactions stabilize coexisting orders from the perspective of GL free energy principle.