Ground States of Low-Dimensional Quantum Antiferromagnets

We have developed a general scheme for carrying out systematic perturbation expansions for groundstate properties of quantum lattice models. As an application, we study the onset of spontaneous Néel order in $S=\frac{1}{2}$ Heisenberg antiferromagnets by expanding around dimerized Hamiltonians. In one dimension (1D) we recover accurately the known exact results. On the square lattice we find novel critical points separating Néel ordered and disordered phases; the estimated critical exponents are consistent with those of the 3D classical Heisenberg model.