THE S=1/2 HEISENBERG-ANTIFERROMAGNET ON THE TRIANGULAR LATTICE - EXACT RESULTS AND SPIN-WAVE THEORY FOR FINITE CELLS

We study the ground state properties of the S = 1/2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (alphaJ) couplings. Classically, this system is known to be ordered in a 120-degrees Neel type state for values - infinity < alpha less-than-or-equal-to 1/8 of the ratio alpha of these couplings and in a collinear state for 1/8 < alpha < 1. The order parameter M and the helicity chi of the 120-degrees structure are obtained by numerical diagonalisation of finite periodic systems of up to N = 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 - infinity < alpha < 1/8. It appears that the SW theory is still valid for the simple triangular HAF (alpha = 0) although the sublattice magnetisation M is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameter N of the collinear order support the previous conjecture of a first order transition between the 120-degrees and the collinear order at alpha congruent-to 1/8.