Long-Range Néel Order in the Triangular Heisenberg Model

Abstract

We have studied the Heisenberg model on the triangular lattice using quantum Monte Carlo techniques (up to 144 sites) and exact diagonalization (up to 36 sites). By studying the spin gap as a function of the system size we have obtained robust evidence for a gapless spectrum, confirming the existence of long-range N\'eel order. Our best estimate is that in the thermodynamic limit the order parameter ${m}^{\ifmmode\dagger\else\textdagger\fi{}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.41\ifmmode\pm\else\textpm\fi{}0.02$ is reduced by about $59%$ from its classical value and the ground state energy per site is ${e}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}0.5458\ifmmode\pm\else\textpm\fi{}0.0001$ in units of the exchange coupling. We have identified the ground state correlations that are important at short distances.