Journal de Physique I · 1996 · 210 citations · 0 references
We have performed a numerical investigation of the ground state properties of\nthe frustrated quantum Heisenberg antiferromagnet on the square lattice\n(``$J_1-J_2$ model''), using exact diagonalization of finite clusters with 16,\n20, 32, and 36 sites. Using a finite-size scaling analysis we obtain results\nfor a number of physical properties: magnetic order parameters, ground state\nenergy, and magnetic susceptibility (at $q=0$). For the unfrustrated case these\nresults agree with series expansions and quantum Monte Carlo calculations to\nwithin a percent or better. In order to assess the reliability of our\ncalculations, we also investigate regions of parameter space with\nwell-established magnetic order, in particular the non-frustrated case $J_2<0$.\nWe find that in many cases, in particular for the intermediate region $0.3 <\nJ_2/J_1 < 0.7$, the 16 site cluster shows anomalous finite size effects.\nOmitting this cluster from the analysis, our principal result is that there is\nN\\'eel type order for $J_2/J_1 < 0.34$ and collinear magnetic order (wavevector\n$\\bbox{Q}=(0,\\pi)$) for $J_2/J_1 > 0.68$. There thus is a region in parameter\nspace without any form of magnetic order. Including the 16 site cluster, or\nanalyzing the independently calculated magnetic susceptibility we arrive at the\nsame conclusion, but with modified values for the range of existence of the\nnonmagnetic region. We also find numerical values for the spin-wave velocity\nand the spin stiffness. The spin-wave velocity remains finite at the\nmagnetic-nonmagnetic transition, as expected from the nonlinear sigma\n