We consider the most general two-site Hamiltonian for a filling of two SU(4) fermions per site (i.e. self-conjugate 6 representation) on the square lattice. First, using a tensor-network approach, we investigate which non-magnetic phases could be stabilized and in which part of the phase diagram [1], and in particular discuss the possibility to realize a topological RVB spin liquid [2]. Then, using a basis transformation, we are able to perform unbiased quantum Monte-Carlo simulations showing the existence of a spin nematic phase and a valence bond crystal one, which are separated by a weak first-order phase transition. Moreover, at the transition, we find an emergent U(1) symmetry which may be due to a nearby deconfined quantum critical point.
[1] O. Gauthé, S. Capponi, M. Mambrini, D. Poilblanc, Phys. Rev. B 101, 205144 (2020)
[2] O. Gauthé, S. Capponi, D. Poilblanc, Phys. Rev. B 101, 205144 (2020)
[3] P. Patil, F. Alet, S. Capponi, M. Mambrini, preprint arXiv:2109.10042