We prove the bound ${\mathit{m}}_{\mathit{s}}$ (\ensuremath{\beta})\ensuremath{\ge} \ensuremath{\surd}3 \ensuremath{\sigma}(\ensuremath{\beta}) between the spontaneous staggered magnetization ${\mathit{m}}_{\mathit{s}}$ (\ensuremath{\beta}) and the long range order parameter \ensuremath{\sigma}(\ensuremath{\beta}) in the quantum Heisenberg antiferromagnets. The same bound has been known for the Heisenberg ferromagnets from the works of Griffiths, and of Dyson, Lieb, and Simon, but extensions to the antiferromagnets had been lacking for more than two decades. When combined with the results on nonvanishing \ensuremath{\sigma}(\ensuremath{\beta}) from the Dyson-Lieb-Simon method, our bound proves the existence of symmetry breaking in the physically natural equilibrium states and ground states obtained by applying an infinitesimal symmetry breaking field.We prove the bound ${\mathit{m}}_{\mathit{s}}$(\ensuremath{\beta})\ensuremath{\ge} \ensuremath{\surd}3 \ensuremath{\sigma}(\ensuremath{\beta}) between the spontaneous staggered magnetization ${\mathit{m}}_{\mathit{s}}$(\ensuremath{\beta}) and the long range order parameter \ensuremath{\sigma}(\ensuremath{\beta}) in the quantum Heisenberg antiferromagnets. The same bound has been known for the Heisenberg ferromagnets from the works of Griffiths, and of Dyson, Lieb, and Simon, but extensions to the antiferromagnets had been lacking for more than two decades. When combined with the results on nonvanishing \ensuremath{\sigma}(\ensuremath{\beta}) from the Dyson-Lieb-Simon method, our bound proves the existence of symmetry breaking in the physically natural equilibrium states and ground states obtained by applying an infinitesimal symmetry breaking field.

Physical Review LettersJan 4, 199320 citations

Néel order versus spin liquid in quantum Heisenberg antiferromagnets on triangular and Kagomé lattices

B. Bernu, P. Lecheminant, C. Lhuillier +1 more

We have realized a thorough quantum mechanical analysis of an extensive number of low lying levels of the Heisenberg Hamiltonian on small periodic samples. Striking qualitative differences appear between the spectra of the triangular lattice and those of the Kagomé lattice. Symmetries and finite size scaling of the low lying levels of the triangular antiferromagnetic point to an à la Néel symmetry breaking, and the dynamical structure factors corroborate this conclusion. The Kagomé antiferromagnet spectra are qualitatively different: no signature of a symmetry breaking has been exhibited and the dynamical structure factors of the low lying levels display broad bands. The Heisenberg antiferromagnet on a Kagomé lattice is a serious candidate for a spin liquid.We have realized a thorough quantum mechanical analysis of an extensive number of low lying levels of the Heisenberg Hamiltonian on small periodic samples. Striking qualitative differences appear between the spectra of the triangular lattice and those of the Kagomé lattice. Symmetries and finite size scaling of the low lying levels of the triangular antiferromagnetic point to an à la Néel symmetry breaking, and the dynamical structure factors corroborate this conclusion. The Kagomé antiferromagnet spectra are qualitatively different: no signature of a symmetry breaking has been exhibited and the dynamical structure factors of the low lying levels display broad bands. The Heisenberg antiferromagnet on a Kagomé lattice is a serious candidate for a spin liquid.

Physica ScriptaJan 1, 199319 citations

Bound states in Heisenberg antiferromagnets

Stephen William Lovesey, Ewald Balcar

Physics Letters ASep 1, 19697 citations

We prove the bound

{\mathit{m}}_{\mathit{s}}

(\ensuremath{\beta})\ensuremath{\ge} \ensuremath{\surd}3 \ensuremath{\sigma}(\ensuremath{\beta}) between the spontaneous staggered magnetization

{\mathit{m}}_{\mathit{s}}

(\ensuremath{\beta}) and the long range order parameter \ensuremath{\sigma}(\ensuremath{\beta}) in the quantum Heisenberg antiferromagnets. The same bound has been known for the Heisenberg ferromagnets from the works of Griffiths, and of Dyson, Lieb, and Simon, but extensions to the antiferromagnets had been lacking for more than two decades. When combined with the results on nonvanishing \ensuremath{\sigma}(\ensuremath{\beta}) from the Dyson-Lieb-Simon method, our bound proves the existence of symmetry breaking in the physically natural equilibrium states and ground states obtained by applying an infinitesimal symmetry breaking field.