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We consider a model Hamiltonian with two SU(4) fermions per site on a squarelattice, showing a competition between bilinear and biquadratic interactions.This model has generated interest due to possible realizations in ultracoldatom experiments and existence of spin liquid ground states. Using a basistransformation, we show that part of the phase diagram is amenable to quantumMonte Carlo simulations without a sign problem. We find evidence for spinnematic and valence bond crystalline phases, which are separated by a weakfirst order phase transition. A U(1) symmetry is found to emerge in the valencebond crystal histograms, suggesting proximity to a deconfined quantum criticalpoint. Our results are obtained with the help of a loop algorithm which allowslarge-scale simulations of bilinear-biquadratic SO(N ) models on arbitrarylattices in a certain parameter regime.

Weakly first-order quantum phase transition between Spin Nematic and Valence Bond Crystal Order in a square lattice SU(4) fermionic model