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

Long-range order and quantum criticality in antiferromagnetic chains with long-range staggered interactions

Jie Ren, Zhao Wang, Weixia Chen +1 more

We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo, and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of quantum phases emerge from the interplay of anisotropy of the long-range exchange interaction and symmetry breaking. We demonstrate nonfrustrating long-range interactions induce the true long-range order in Heisenberg antiferromagnetic chains with a continuous symmetry breaking, lifting the restrictions imposed by the Mermin-Wagner theorem.We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo, and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of quantum phases emerge from the interplay of anisotropy of the long-range exchange interaction and symmetry breaking. We demonstrate nonfrustrating long-range interactions induce the true long-range order in Heisenberg antiferromagnetic chains with a continuous symmetry breaking, lifting the restrictions imposed by the Mermin-Wagner theorem.

arXiv:2203.11032Physical review. EMar 21, 20228 citations

Long Range Order in Antiferromagnetic Quantum Spin Systems

之康尾関, Yukiyasu Ozeki

Jan 1, 19890 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.