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

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