Xu Hong-Ze, Zhang Shun-Yao, Guo Guang-Can, Gong Ming
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.
Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China.
Sci Rep. 2021 Mar 19;11(1):6462. doi: 10.1038/s41598-021-85483-0.
We report the exact dimer phase, in which the ground states are described by product of singlet dimer, in the extended XYZ model by generalizing the isotropic Majumdar-Ghosh model to the fully anisotropic region. We demonstrate that this phase can be realized even in models when antiferromagnetic interaction along one of the three directions. This model also supports three different ferromagnetic (FM) phases, denoted as x-FM, y-FM and z-FM, polarized along the three directions. The boundaries between the exact dimer phase and FM phases are infinite-fold degenerate. The breaking of this infinite-fold degeneracy by either translational symmetry breaking or [Formula: see text] symmetry breaking leads to exact dimer phase and FM phases, respectively. Moreover, the boundaries between the three FM phases are critical with central charge [Formula: see text] for free fermions. We characterize the properties of these boundaries using entanglement entropy, excitation gap, and long-range spin-spin correlation functions. These results are relevant to a large number of one dimensional magnets, in which anisotropy is necessary to isolate a single chain out from the bulk material. We discuss the possible experimental signatures in realistic materials with magnetic field along different directions and show that the anisotropy may resolve the disagreement between theory and experiments based on isotropic spin-spin interactions.
我们通过将各向同性的马宗达 - 戈什模型推广到完全各向异性区域，在扩展的XYZ模型中报告了精确的二聚体相，其中基态由单重态二聚体的乘积描述。我们证明，即使在沿三个方向之一存在反铁磁相互作用的模型中，这个相也能实现。该模型还支持三种不同的铁磁（FM）相，分别表示为x - FM、y - FM和z - FM，它们沿三个方向极化。精确二聚体相和FM相之间的边界是无限简并的。通过平移对称性破缺或[公式：见原文]对称性破缺分别打破这种无限简并，会导致精确二聚体相和FM相。此外，三个FM相之间的边界对于自由费米子是具有中心荷[公式：见原文]的临界边界。我们使用纠缠熵、激发能隙和长程自旋 - 自旋关联函数来表征这些边界的性质。这些结果与大量一维磁体相关，在这些磁体中，各向异性对于从块状材料中分离出单链是必要的。我们讨论了在沿不同方向施加磁场的实际材料中可能的实验特征，并表明各向异性可能解决基于各向同性自旋 - 自旋相互作用的理论与实验之间的分歧。
