Long-range order without broken symmetry: Two-dimensional Heisenberg antiferromagnet at zero temperature

We have calculated the probability distribution for staggered magnetization at T=0 for the two-dimensional (2D) antiferromagnetic Heisenberg model (2D AFH) on a series of finite lattices up to 26 sites. We find that the singlet ground state of the 2D AFH possesses long-range magnetic order without broken symmetry. We also study the lowest triplet state and find that it becomes degenerate with the ground state in the thermodynamic limit. This state does exhibit broken symmetry on a finite lattice. The value of the staggered magnetization in the thermodynamic limit is also obtained by extrapolation. We compare our results with the results obtained by other methods and discuss the relevance to the high-$T_c$ superconductive oxide compounds.