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We study a variational wave function for the ground state of thetwo-dimensional S=1/2 Heisenberg antiferromagnet in the valence bond basis. Theexpansion coefficients are products of amplitudes h(x,y) for valence bondsconnecting spins separated by (x,y) lattice spacings. In contrast to previousstudies, in which a functional form for h(x,y) was assumed, we here optimizeall the amplitudes for lattices with up to 32*32 spins. We use two differentschemes for optimizing the amplitudes; a Newton/conjugate-gradient method and astochastic method which requires only the signs of the first derivatives of theenergy. The latter method performs significantly better. The energy for largesystems deviates by only approx. 0.06% from its exact value (calculated usingunbiased quantum Monte Carlo simulations). The spin correlations are also wellreproduced, falling approx. 2% below the exact ones at long distances. Theamplitudes h(r) for valence bonds of long length r decay as 1/r^3. We alsodiscuss some results for small frustrated lattices.Comment: v2: 8 pages, 5 figures, significantly expanded, new optimization  method, improved result

Variational ground states of two-dimensional antiferromagnets in the valence bond basis