Independent Bond Fluctuation Approximation to the Ground State of Quantum Antiferromagnets

A simple approach to estimation of the ground state energy of quantum antiferromagnets is developed, based on the approximation that quantum fluctuations around different bonds are independent. The ground state energy estimates are as good as spin wave theory or slightly better. A canonical transformation of the spin operators to generate bond quantum fluctuations is devised and applied to the classical ground state of the $S=\frac{1}{2}$ Heisenberg model on the square lattice. This simple picture of quantum spin fluctuations might be useful in more complex models. The resulting nearest neighbor and next-nearest neighbor correlations can be used in an alternative derivation of spin waves in the Heisenberg model, giving an accurate dispersion as well as raising and lowering operators.