Static properties of a quasi one-dimensional antiferromagnet in magnetic field

We calculate the effect of zero-point fluctuations on the magnetostatic properties of a quasi one-dimensional antiferromagnetic helimagnet with and without in-plane anisotropy. We find substantial reduction of the uniform susceptibility and the sublattice magnetization from their classical values and appreciable renormalization of the spin-flop field at $T=0$. The magnetization curve varies nonlinearly at small fields and is described by a universal formula at high fields. The results are compared with numerical simulations on one-dimensional systems and measurements in the CsNiCl$_3$-type compounds.