Spin stiffnesses of the quantum Heisenberg antiferromagnet on a triangular lattice

Abstract

The two spin stiffnesses (\ensuremath{\rho}\ensuremath{\parallel},\ensuremath{\rho}\ensuremath{\perp}) of the quantum Heisenberg antiferromagnet on the triangular lattice are investigated by a first-order spin-wave theory. At the thermodynamic limit, spin-wave calculations predict a large reduction of the spin stiffnesses by quantum fluctuations: relative to their classical values, the reduction is 68% for ${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\parallel}}}$, 12% for ${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\perp}}}$, and 40% for the average spin stiffness ${\mathrm{\ensuremath{\rho}}}_{\mathit{m}}$. In this approach quantum fluctuations, not large enough to destroy the rigidity of N\'eel order, are nevertheless changing the sign of the anisotropy of the spin stiffnesses tensor. A method using exact diagonalizations on finite lattices is used to countercheck the importance of quantum fluctuations on small sizes. These last results confirm qualitatively the conclusions of the first-order spin-wave calculation.