Eur. Phys. J. B 73, 117-124 (2010)
https://doi.org/10.1140/epjb/e2009-00400-4

The spin-1/2 J₁–J₂ Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N = 40 spins

¹ Institut für Theoretische Physik, Universität Magdeburg, 39016 Magdeburg, Germany
² Universitätsrechenzentrum, Universität Magdeburg, 39016 Magdeburg, Germany

Corresponding author: johannes.richter@physik.uni-magdeburg.de

Received: 18 September 2009
Published online: 25 November 2009

Abstract

We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J₁-J₂ Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J₂/J₁. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J₂ < J₂^c₁ and J₂ > J₂^c₂ separated by a gapful quantum paramagnetic phase. We estimate J₂^c₁ ≈ 0.35J₁ and J₂^c₂ ≈ 0.66J₁.