Schwinger boson theory of the J1,J2=J3 kagome antiferromagnet

TL;DR

This paper employs Schwinger-boson mean-field theory to analyze the phase diagram of the J1,J2=J3 kagome antiferromagnet, revealing the stability of a spin liquid phase and its transition to chiral order.

Contribution

It introduces a detailed phase diagram for the kagome antiferromagnet using Schwinger-boson theory and provides an exact ground state solution on a Husimi cactus.

Findings

Spin liquid remains stable up to J=1/3.

Transition from spin liquid to chiral order at J=1/2.

Exact ground state solution on Husimi cactus.

Abstract

We study the kagome antiferromagnet for quantum spin-1/2 with first J1, second J2 and third J3 neighbour exchanges, along the J2 = J3 = J line. We use Schwinger-boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at J = 0 remains essentially stable over a large window, up to J = 1/3, because it is only weakly frustrated by the J term. Then at J = 1/2, the intermediate Z2 spin liquid condenses into a long-range chiral order because of the change of nature of local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus.