Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice

TL;DR

This paper investigates a complex twelve-sublattice ordered phase in the J1-J2 kagome lattice model, revealing its classical and quantum stability, symmetry properties, and the effects of thermal and quantum fluctuations.

Contribution

It provides a detailed analysis of the classical and quantum phases of the J1-J2 kagome model, identifying the stability range of the twelve-sublattice order and the nature of symmetry breaking.

Findings

Classical ground state exhibits twelve non-coplanar sublattices with cuboctahedral symmetry.

Quantum fluctuations destabilize the classical order beyond a small J2/|J1| ratio.

The phase is gapped and persists at finite temperature due to Z2 symmetry breaking.

Abstract

Motivated by recent experiments on an S=1/2 antiferromagnet on the kagome lattice, we investigate the Heisenberg J1-J2 model with ferromagnetic J1 and antiferromagnetic J2. Classically the ground state displays Neel long range order with 12 non-coplanar sublattices. The order parameter has the symmetry of a cuboctahedron so that it fully breaks SO(3) as well as the spin-flip symmetry, and we expect from the latter a Z2 symmetry breaking pattern. As might be expected from the Mermin-Wagner theorem in two dimensions, the SO(3) symmetry is restored by thermal fluctuations while the Z2 symmetry breaking persists up to a finite temperature. A complete study of S=1/2 exact spectra reveals that the classical order subsists for quantum spins in a finite range of parameters. First order spin wave calculations give the range of existence of this phase and the renormalisations at T=0 of the order parameters associated to both symmetry breakings. This phase is destroyed by quantum fluctuations for a small but finite J2/|J1|\simeq3 consistently with exact spectra studies which indicate a gapped phase.