Phase Diagram of the One Dimensional $S=1/2$ $XXZ$ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions

TL;DR

This paper investigates the phase diagram of a one-dimensional $S=1/2$ $XXZ$ model with competing ferromagnetic and antiferromagnetic interactions using quantum renormalization group techniques, revealing multiple quantum phases.

Contribution

It applies second order quantum renormalization group to analyze the phase diagram of a complex $XXZ$ model with competing interactions, identifying various quantum and classical phases.

Findings

Identification of quantum spin-fluid and dimer phases.

Mapping of phase boundaries in phase space.

Use of QRG to analyze stability of phases.

Abstract

We have studied the phase diagram of the one dimensional $S=1/2$ $XXZ$ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest neighbor interactions. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points and the running of coupling constants. The second order QRG has been implemented to get the self similar Hamiltonian. This model shows a rich phase diagram which consists of different phases which possess the quantum spin-fluid and dimer phases in addition to the classical N\'{e}el and ferromagnetic ones. The border between different phases has been shown as a projection onto two different planes in the phase space.