Phase diagram of the one-dimensionalS=12XXZmodel with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions

Abstract

We have studied the phase diagram of the one-dimensional $S=\frac{1}{2}$ $XXZ$ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We have applied the quantum renormalization group (QRG) approach to obtain stable fixed points and the scaling of coupling constants. The QRG prescription has to be implemented to the second order of interblock interactions to obtain a self-similar Hamiltonian after each step of the QRG. This model shows a rich phase diagram which includes quantum spin-fluid and dimer phases in addition to the classical N\'eel and ferromagnetic ones. We have found the border between different phases by tracing the scaling of coupling constants.