1994/02/28 by H. J. Schulz, Timothy Ziman, T. A. L. Ziman +2 · 2 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1051/jp1:1996236
published as J. Physique I, 6, 675 (1996) · 34 pages, RevTeX 3.0, figures appended in uuencoded form
arxiv created 1994/03/30 · openalex publication_date 1996/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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). For the unfrustrated case these results agree with series expansions and quantum Monte Carlo calculations to within a percent or better. 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 N'eel type order for J2/J1 < 0.34 and collinear magnetic order (wavevector \bboxQ=(0,π)) for J2/J1 > 0.68. There thus is a region in parameter space without any form of magnetic order. Including the 16 site cluster, or analyzing the independently calculated magnetic susceptibility we arrive at the same conclusion, but with modified values for the range of existence of the nonmagnetic region. We also find numerical values 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