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

Abstract: 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.