Quantum fluctuations and anisotropy in quasi-one-dimensional antiferromagnets

In the quasi-one-dimensional antiferromagnets CsMnBr${}_3$ and RbMnBr${}_3$ the magnetization produced by an external magnetic field displays a much stronger dependence upon the direction of the field than expected from calculations done for a system of classical spins at zero temperature. By performing these calculations for a system at the temperature at which experiments were made it has been shown that thermal fluctuations may account for the observed anisotropy of the magnetization. We analyze here the role of quantum fluctuations. We find that the spin-wave approximation does not give meaningful results when applied to these systems and explain why this is so. We perform then density-matrix renormalization-group calculations, which show that the anisotropy is enhanced over its classical value by quantum fluctuations already at $T=0\mathrm{}$.