MAGNETIC ORDER AND DISORDER IN THE FRUSTRATED QUANTUM HEISENBERG-ANTIFERROMAGNET IN 2 DIMENSIONS

We have performed a numerical investigation of the ground state proper ties of the frustrated quantum Heisenberg antiferromagnet on the squar e lattice (''J(1) - J(2) model''), using exact diagonalization of fini te clusters with 16, 20, 32, and 36 sites. Using a finite-size scaling analysis we obtain results for a number of physical properties: magne tic order parameters, ground state energy, and magnetic susceptibility (at q = 0). In order to assess the reliability of our calculations, w e also investigate regions of parameter space with well-established ma gnetic order, in particular the non-frustrated case J(2) < 0. We find that in many cases, in particular for the intermediate region 0.3 < J( 2)/J(1) < 0.7, the 16 site cluster shows anomalous finite size effects . Omitting this cluster from the analysis, our principal result is tha t there is Neel type order for J(2)/J(1) < 0.34 and collinear magnetic order (wavevector Q = (0, pi)) for J(2)/J(1) > 0.68. An error analysi s indicates uncertainties of order +/-0.04 in the location of these cr itical values of J(2). There thus is a region in parameter space witho ut any form of magnetic order. For the unfrustrated case the results f or order parameter, ground state energy, and susceptibility agree with series expansions and quantum Monte Carlo calculations to within a pe rcent or better. Including the 16 site cluster, or analyzing the indep endently calculated magnetic susceptibility we also find a nonmagnetic region, but with modified values for the range of existence of the no nmagnetic region. From the leading finite-size corrections we also obt ain results for the spin-wave velocity and the spin stiffness. The spi n-wave velocity remains finite at the magnetic-nonmagnetic transition, as expected from the nonlinear sigma model analogy.