Quantum Fluctuations in the Annni Model

Abstract

We obtain the ANNNI model from a Heisenberg model with large single--ion anisotropy energy, $D$, as might be relevant for helical spin systems. We treat quantum fluctuations to lowest order in $1/S$ at zero temperature within an expansion in $J/D$, where $J$ is an exchange energy. The transition from the state with periodicity $p=4$ to the uniform state ($p= \infty$) occurs via an infinite sequence of first order transitions in which $p$ increases monotonically.