Analysis of the ground-state wave function of theJ 1-J 2 quantum Heisenberg antiferromagnet

Abstract

We investigate the ground-state wave function $$|\psi \rangle = \sum\limits_n {\alpha _n } |n\rangle $$ of the spin-1/2J 1-J 2 model on finite square lattices ofN=16(4×4) andN=24(4×6) sites. We find that the Marshall-Peierls phase rule for coefficientsα n , which was derived for unfrustrated bipartite lattices (J 2=0), holds exactly for comparably large frustration up toJ 2/J 1=0.28 (N=16) and up toJ 2/J 1=0.20 (N=24). But even for strong frustration up toJ 2/J 1≈0.45 the Marshall-Peierls rule describes the phase relationships in the ground state excellently. In the region of dominatingJ 2 a phase rule can be formulated as a product of the rules for two independent antiferromagnets. We find that the violation of the Marshall-Peierls sign rule does not dramatically affect the order parameters up toJ 2/J 1≈0.6. To calculate the magnitude of the coefficientsα n by a variational procedure we search for a represantative relationship between theα n and (a few) parametersP 1,n ...P k, n classifying the Ising basis states |n>. By comparison with the exact ground state we analyze classification schemes based on pair correlations (Jastrow type wave functions) as well as schemes taking into account cluster parameters. While for small frustrationJ 2/J 1<0.2 a short-range Jastrow description (nearest-neighbour and next nearestneighbour pairing) seems to be sufficient for the adequate description of the ground state one definitly needs longrange pairing and/or cluster parameters to construct a reasonable trial wave function for strong frustration. As an example for a special Jastrow type wave function we discuss an ansatz coming from the spin-wave theory. Finally, we consider the influence of the anisotropic exchangeJ zz ≠J xx ,J yy on the quality of the short-range Jastrow wave function and find and excellent agreement with the exact ground state already for Ising exchange anisotropiesJ xx =J yy ≈0.5J zz .