Magnetic Order and Disorder in the Frustrated Quantum Heisenberg Antiferromagnet in Two Dimensions
Résumé
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,π)) for J2/J1>0.68. An error analysis indicates uncertainties of order ±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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