Spin-1/2 quantum antiferromagnets on the triangular lattice

Abstract

The spin-1/2 anisotropic Heisenberg antiferromagnet is studied at T=0 on the triangle lattice via numerical diagonalization for system sizes up to N=36 sites. Extrapolation to the thermodynamic limit suggests that the isotropic system possesses no, or very small, \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 magnetic order; no helical or chiral order; and spin-spin correlations consistent with that of a critical phase. For XY-like anisotropy there is long-ranged \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 magnetic order. In contrast to bipartite lattices, the standard first- and second-order spin-wave theories are not quantitatively accurate. Excitation energy gaps suggest that the lowest lying excitations for the isotropic point are not spin-flip excitations in the thermodynamic limit. The results for the isotropic point appear to agree with recent series expansion, large-N expansion, and the original resonating valence bond picture of Anderson, although they cannot be considered as conclusive evidence supporting any of these theories.