SU(N) Heisenberg model on the square lattice: A continuous-N quantum Monte Carlo study

A quantum phase transition is typically induced by tuning an external parameter that appears as a coupling constant in the Hamiltonian. Another route is to vary the global symmetry of the system, generalizing, e.g., SU(2) to SU(N). In that case, however, the discrete nature of the control parameter prevents one from identifying and characterizing the transition. We show how this limitation can be overcome for the SU(N) Heisenberg model with the help of a singlet projector algorithm that can treat N continuously. On the square lattice, we find a direct, continuous phase transition between Néel-ordered and crystalline bond-ordered phases at N_c=4.57(5) with critical exponents z=1 and β/ν=0.81(3).