Variational ground states of 2D antiferromagnets in the valence bond basis

Abstract

We study a variational wave function for the ground state of the two-dimensional S=1/2 Heisenberg antiferromagnet in the valence bond basis. The expansion coefficients are products of amplitudes h(x,y) for valence bonds connecting spins separated by (x,y) lattice spacings. In contrast to previous studies, in which a functional form for h(x,y) was assumed, we here optimize all the amplitudes for lattices with up to 32*32 spins. We use two different schemes for optimizing the amplitudes; a Newton/conjugate-gradient method and a stochastic method which requires only the signs of the first derivatives of the energy. The latter method performs significantly better. The energy for large systems deviates by only approx. 0.06% from its exact value (calculated using unbiased quantum Monte Carlo simulations). The spin correlations are also well reproduced, falling approx. 2% below the exact ones at long distances. The amplitudes h(r) for valence bonds of long length r decay as 1/r^3. We also discuss some results for small frustrated lattices.

v2: 8 pages, 5 figures, significantly expanded, new optimization method, improved results

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• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
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Cited by in corpus (9)

• Variational quantum Monte Carlo simulations with tensor-network states
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Master equation approach to computing RVB bond amplitudes
• Simulating a two-dimensional frustrated spin system with fermionic resonating-valence-bond states
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Correlated valence-bond states
• Definitions of entanglement entropy of spin systems in the valence-bond basis
• Generalized mean field description of entanglement in dimerized spin systems
• Comment on "Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets"