Critical properties of a one-dimensional frustrated quantum magnetic model

Abstract

The phase diagram and ground-state energy along the phase boundary are estimated for a one-dimensional spin-½ Ising model with competing nearest-and next-nearest-neighbor interactions in presence of a transverse field. We have used a self-consistent Hartree-Fock approximation and a real-space renormalization-group treatment. The phase diagram (of this one-dimensional quantum model) is compared to that of a two-dimensional classical axial next-nearest-neighbor model and the Lifshitz point is located. The estimated ground-state energy, along the critical line, is seen to reduce considerably (like the critical fields), with increasing competition, showing the effect of frustration.