Neel state of antiferromagnet as a result of a local measurement in the distributed quantum system

Single-site measurement in a distributed macroscopic antiferromagnet is considered; we show that it can create antiferromagnetic sublattices at macroscopic scale. We demonstrate that the result of measurement depends on the symmetry of the ground state: for the easy-axis case the Neel state is formed, while for the easy-plane case unusual ``fan'' sublattices appear with unbroken rotational symmetry, and a decoherence wave is generated. For the latter case, a macroscopically large number of measurements is needed to pin down the orientation of the sublattices, in spite of the high degeneracy of the ground state. We note that the type of the final state and the appearance of the decoherence wave are governed by the degree of entanglement of spins in the system.