The dynamical structure factor of the SU(4) algebraic spin liquid on the honeycomb lattice

We compute the momentum resolved dynamical spin structure factor $S(k,\omega)$ of the SU(4) Heisenberg model on the honeycomb lattice assuming the $\pi$-flux Dirac spin liquid ground state by two methods: (i) variationally using Gutzwiller projected particle-hole excitations of the $\pi$-flux Fermi sea and (ii) in the non-interacting parton mean-field picture. The two approaches produce qualitatively similar results. Based on this analogy, we argue that the energy spectrum of the projected excitations is a gapless continuum of fractional excitations. Quantitatively, the Gutzwiller projection shifts the weight from higher to lower energies, thus emphasizing the lower edge of the continuum. In the mean-field approach, we obtained the $1/\text{distance}^4$ decay of the spin correlation function, and the local correlations show $S^{33}_{\text{MF}}(\omega)\propto \omega^3$ behavior.