Algebraic spin liquid in the SU(6) Heisenberg model on the kagome lattice

We explore the Dirac spin liquid (DSL) as a candidate for the ground state of the Mott insulating phase of fermions with six flavors on the kagome lattice, particularly focusing on realizations using $^{173}\mathrm{Yb}$ atoms in optical lattices. Using mean-field theory and variational Monte Carlo simulations, we demonstrate that the DSL has the lowest variational energy among SU(6) symmetry-preserving trial wave functions with a periodicity of a 12-site unit cell, as well as uniform chiral states with larger unit cells. It remains a local minimum even when small second-nearest neighbor and ring-exchange interactions are introduced. To characterize the DSL, we calculate the static and dynamic structure factor of the Gutzwiller projected wave function and compare it with mean-field calculations. The static structure factor shows triangular-shaped plateaus around the $\mathrm{K}$ points in the extended Brillouin zone, with small peaks at the corners of these plateaus. The dynamical structure factor consists of a gapless continuum of fractionalized excitations. Our study also presents several complementary results, including bounds for the ground-state energy, methods for calculating three-site ring-exchange expectations in the projective mean field, the boundary of ferromagnetic states, and the nontopological nature of flat bands in the DSL band structure.