SU(N) quantum spin models:: a variational wavefunction study

SU(N) quantum spin systems may be realized in a variety of physical systems including ultracold atoms in optical lattices. The study of such models also leads to insights into possible novel quantum phases and phase transitions of SU(2) spin models. Here we use Gutzwiller projected fermionic variational wavefunctions to explore the phase diagram and correlation functions of SU(N) quantum spin models in the self-conjugate representation. In one dimension, the ground state of the SU(4) spin chain with Heisenberg bilinear and biquadratic interactions is studied by examining instabilities of the Gutzwiller projected free fermion ground state to various broken symmetries. The variational phase diagram so obtained agrees well with exact results. The spin-spin and dimer-dimer correlation functions of the Gutzwiller projected free fermion state with N flavours of fermions are in good agreement with exact and 1/N calculations for the critical points of SU(N) spin chains. In two dimensions, the phase diagram of the antiferromagnetic Heisenberg model on the square lattice is obtained by finding instabilities of the Gutzwiller projected p-flux state. In the absence of biquadratic interactions, the model exhibits long-range Neel order for N = 2 and 4, and spin Peierls (columnar dimer) order for N > 4. Upon including biquadratic interactions in the SU(4) model (with a sign appropriate to a fermionic Hubbard model), the Neel order diminishes and eventually disappears, giving way to an extended valence bond crystal. In the case of the SU(6) model, the dimerized ground state melts at sufficiently large biquadratic interaction, yielding a projected pi-flux spin liquid phase which in turn undergoes a transition into an extended valence bond crystal at even larger biquadratic interaction. The spin correlations of the projected pi-flux state at N = 4 are in good agreement with 1/N calculations. We find that the state shows strongly enhanced dimer correlations, in qualitative agreement with recent theoretical predictions. We also compare our results with a recent quantum Monte Carlo study of the SU(4) Heisenberg model.