Trion states and quantum criticality of attractive SU(3) Dirac fermions

We perform the projector quantum Monte Carlo (QMC) simulation to study the trion formation and quantum phase transition in the half-filled attractive SU(3) Hubbard model on a honeycomb lattice. With increasing attractive Hubbard interaction, our simulations demonstrate a continuous quantum phase transition from the semimetal to charge density wave (CDW) at the critical coupling $U_c/t=-1.52(2)$. The critical exponents $\nu=0.82(3)$ and $\eta=0.58(4)$ determined by the QMC simulation remarkably disagree with those of the $N=3$ chiral Ising universality class suggested by the effective Gross-Neveu-Yukawa (GNY) theory, but coincide with the $N=1$ chiral Ising universality class. In the CDW phase, we show that on-site and off-site trions coexist and the off-site trion forms a local bond state. Our work not only illustrates the formation of off-site trions in two-dimensional Hubbard model, but also raises doubts about the extent of applicability of GNY model on the attractive SU(3) Dirac fermions.