Weakly first-order quantum phase transition between spin-nematic and valence-bond crystal order in a square-lattice SU(4) fermionic model

We consider a model Hamiltonian with two SU(4) fermions per site on a square lattice, showing a competition between bilinear and biquadratic interactions. This model has generated interest due to possible realizations in ultra-cold-atom experiments and existence of spin-liquid ground states. Using a basis transformation, we show that part of the phase diagram is amenable to quantum Monte Carlo simulations without a sign problem. We find evidence for spin nematic and valence-bond crystalline phases, which are separated by a weak first-order phase transition. A U(1) symmetry is found to emerge in the valence-bond crystal histograms, suggesting proximity to a deconfined quantum critical point. Our results are obtained with the help of a loop algorithm which allows large-scale simulations of bilinear-biquadratic SO(N) models on arbitrary lattices in a certain parameter regime.

Automated summary

We consider a model Hamiltonian with two SU(4) fermions per site on a square lattice, showing a competition between bilinear and biquadratic interactions. Using a basis transformation, we show that part of the phase diagram can be simulated with quantum Monte Carlo simulations without a sign problem. Evidence for spin nematic and valence-bond crystalline phases is found, with a weak first-order phase transition separating them. An emergent U(1) symmetry is observed in the valence-bond crystal histograms, suggesting proximity to a deconfined quantum critical point. Our results are obtained using a loop algorithm that allows large-scale simulations of bilinear-biquadratic SO(N) models on arbitrary lattices in a certain parameter regime.