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

Abstract

SU(N) quantum spin systems may be realized in a variety of physical systems includingultracold atoms in optical lattices. The study of such models also leadsto insights into possible novel quantum phases and phase transitions ofSU(2) spin models. Here we use Gutzwiller projected fermionic variationalwavefunctions to explore the phase diagram and correlation functions ofSU(N) quantum spin models in the self-conjugate representation. In one dimension, the ground state of theSU(4) spin chain with Heisenberg bilinear and biquadratic interactions is studied by examininginstabilities 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–spinand dimer–dimer correlation functions of the Gutzwiller projected free fermion state withN flavours of fermions are in good agreement with exact and1/N calculations for thecritical points of SU(N) spin chains. In two dimensions, the phase diagram of the antiferromagnetic Heisenbergmodel on the square lattice is obtained by finding instabilities of the Gutzwiller projectedπ-flux state. In the absence of biquadratic interactions, the model exhibits long-range Néel order forN = 2 and 4, and spin Peierls (columnar dimer) order forN>4. Upon including biquadratic interactions in theSU(4) model (with a sign appropriate to a fermionic Hubbard model), the Néel order diminishes andeventually disappears, giving way to an extended valence bond crystal. In the case of theSU(6) model, the dimerized ground state melts at sufficiently large biquadratic interaction, yielding a projectedπ-flux spin liquid phase which in turn undergoes a transition into an extended valence bondcrystal at even larger biquadratic interaction. The spin correlations of the projectedπ-flux state atN = 4 are in goodagreement with 1/N calculations. We find that the state shows strongly enhanced dimer correlations,in qualitative agreement with recent theoretical predictions. We alsocompare our results with a recent quantum Monte Carlo study of theSU(4) Heisenberg model.