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Using linear flavor-wave theory (LFWT) and auxiliary field quantum MonteCarlo (QMC), we investigate the properties of the SU(4) Heisenberg model on theanisotropic square lattice in the fully antisymmetric six-dimensionalirreducible representation, a model that describes interacting fermions withfour flavors at half-filling. Thanks to the calculations on very large systems,we have been able to convincingly demonstrate that QMC results are consistentwith a small but finite antiferromagnetic moment at the isotropic point, inqualitative agreement with LFWT obtained earlier [F. H. Kim {\it{et al.}},Phys. Rev. B {\bf 96}, 205142 (2017)], and in quantitative agreement withresults obtained previously on the Hubbard model [D. Wang {\it{et al.}}, Phys.Rev. Lett. {\bf 112}, 156403 (2014)] after extrapolation to infinite $U/t$. Thepresence of a long-range antiferromagnetic order has been further confirmed byshowing that a phase transition takes place into a valence-bond solid (VBS)phase not too far from the isotropic point when reducing the coupling constantalong one direction on the way to decoupled chains.

physical review. b./physical review. b

Dimensional crossover in the SU(4) Heisenberg model in the  six-dimensional antisymmetric self-conjugate representation revealed by  quantum Monte Carlo and linear flavor-wave theory