Frustrated ferromagnetic spin-1/2 chain in the magnetic field

TL;DR

This paper investigates the ground state and magnetization properties of a frustrated ferromagnetic spin-1/2 chain under magnetic field, using approximate methods to reveal quantum effects near phase transitions.

Contribution

It introduces two approximate methods to analyze the frustrated spin chain and compares their results, highlighting quantum fluctuations' impact on critical behavior.

Findings

Quantum fluctuations alter classical critical exponents.

Magnetization behavior varies near and far from the transition point.

Results relate to experimental magnetization curves in $Rb_{2}Cu_{2}Mo_{3}O_{12}$.

Abstract

We study the ground state properties of the Heisenberg spin-1/2 chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions using two approximate methods. One of them is the Jordan-Wigner mean-field theory and another approach based on the transformation of spin operators to bose-ones and on the variational treatment of bosonic Hamiltonian. Both approaches give close results for the ground state energy and the T=0 magnetization curve. It is shown that quantum fluctuations change the classical critical exponents in the vicinity of the transition point from the ferromagnetic to the singlet ground state. The magnetization process displays the different behavior in the regions near and far from the transition point. The relation of the obtained results to experimental magnetization curve in $Rb_{2}Cu_{2}Mo_{3}O_{12}$ is discussed.