Two-dimensional frustrated Heisenberg model: Variational study

TL;DR

This paper investigates the stability of the ferromagnetic phase in a 2D quantum spin-1/2 model with competing interactions, using a novel variational approach based on boson representation to accurately determine phase transition points.

Contribution

It introduces a new variational method based on boson representation, providing precise estimates of transition points and insights into the phase transition character.

Findings

Different exchange integral values destabilize the ferromagnetic state for one and two magnon excitations.

Classical approximation is inadequate for studying the transition in 2D.

The new variational approach yields accurate transition point estimates.

Abstract

The stability of the ferromagnetic phase of the 2D quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnon are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function of new type. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain the accurate estimate of the transition point and to study the character of the phase transition.