TheS=1/2 Heisenberg antiferromagnet on the triangular lattice: Exact results and spin-wave theory for finite cells

We study the ground state properties of theS=1/2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (αJ) couplings. Classically, this system is known to be ordered in a 120° Néel type state for values-∞<α≦1/8 of the ratio α of these couplings and in a collinear state for 1/8<α<1. The order parameter ℳ and the helicity /gC of the 120° structure are obtained by numerical diagonalisation of finite periodic systems of up toN=30 sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region-∞<α<1/8. It appears that the SW theory is still valid for the simple triangular HAF (α=0) although the sublattice magnetisation ℳ is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameterM of the collinear order support the previous conjecture of a first order transition between the 120° and the collinear order at α≅1/8.