An exact evaluation of the occurrence of helical order in the quantum annnh model

It is customary to use the classical approximation for studying magnetic helical configurations. Recently, Harris and Rastelli performed a T-matrix calculation in order to take into account long-wavelength quantum fluctuations exactly in a hexagonal lattice with competing exchange interactions up to third neighbours in the basal plane. Interesting new features such as a first-order phase transition between the helix and ferromagnetic phases were found. Here the authors apply that approach to an axial next-nearest-neighbour Heisenberg model, (ANNNH), the quantum version of the well known ANNNI model of Fisher and Selke (1980). They find that in the ANNNH model, quantum fluctuations do not change the location or the order of the ferro-helix phase transition found in the classical limit (S to infinity) for any S=¹/₂, even in the extreme 1D limit (linear chain). For S=¹/₂ they cannot produce results by the same method because the coefficient that should, if positive, ensure the stability of the ferromagnetic phase vanishes.