J. Phys. I France
Volume 6, Numéro 5, May 1996
Page(s) 675 - 703
DOI: 10.1051/jp1:1996236
J. Phys. I France 6 (1996) 675-703

Magnetic Order and Disorder in the Frustrated Quantum Heisenberg Antiferromagnet in Two Dimensions

H.J. Schulz1, T.A.L. Ziman2 and D. Poilblanc2

1  Laboratoire de Physique des Solides, Laboratoires associés au CNRS, Université Paris-Sud, 91405 Orsay, France
2  Laboratoire de Physique Quantique, Laboratoire associés au CNRS, Université Paul Sabatier, 31602 Toulouse, France

(Received 13 October 1995, received in final form 11 January 1996, accepted 22 January 1996)

We have performed a numerical investigation of the ground state properties of the frustrated quantum Heisenberg antiferromagnet on the square lattice (" J1-J2 model"), using exact diagonalization of finite clusters with 16, 20, 32, and 36 sites. Using a finite-size scaling analysis we obtain results for a number of physical properties: magnetic order parameters, ground state energy, and magnetic susceptibility (at q=0). In order to assess the reliability of our calculations, we also investigate regions of parameter space with well-established magnetic order, in particular the non-frustrated case J2 <0. We find that in many cases, in particular for the intermediate region 0.3<J2/J1<0.7, the 16 site cluster shows anomalous finite size effects. Omitting this cluster from the analysis, our principal result is that there is Néel type order for J2/J1<0.34 and collinear magnetic order (wavevector Q $=(0,\pi)$) for J2/J1>0.68. An error analysis indicates uncertainties of order $\pm 0.04$ in the location of these critical values of J2. There thus is a region in parameter space without any form of magnetic order. For the unfrustrated case the results for order parameter, ground state energy, and susceptibility agree with series expansions and quantum Monte Carlo calculations to within a percent or better. Including the 16 site cluster, or analyzing the independently calculated magnetic susceptibility we also find a nonmagnetic region, but with modified values for the range of existence of the nonmagnetic region. From the leading finite-size corrections we also obtain results for the spin-wave velocity and the spin stiffness. The spin-wave velocity remains finite at the magnetic-nonmagnetic transition, as expected from the nonlinear sigma model analogy.

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