体电极化的强度作为表征拓扑量子物质的非定域序参量。最近的一篇论文[H。Watanabe \textit{et al.}，Phys. Rev. B { \bf 103}，134430（2021）]，我们讨论了一维量子自旋系统中体极化的磁模拟，即一维量子自旋系统边缘上的量子化磁化，边缘磁化与拓扑奇自旋Half相的分数边缘态共享拓扑原点.尽管有这种拓扑起源，边缘磁化也可以出现在拓扑平凡的量子相位。我们开发简单的场理论参数，解释边缘磁化的特性。场论表明，U（1）自旋旋转对称性和位心或键心反转对称性保护了边缘磁化的量子化。我们继续讨论，非零磁化平台上的量子相位也可以有量子化的边缘磁化，偏离在体的磁化密度。我们证明了量子化的边缘磁化区分两个量子相位上的磁化高原分离的量子临界点。边缘磁化在量子临界点处呈现从零到$1/2$的突然阶跃变化，因为量子相变发生在保护边缘磁化的量化的对称性的存在下。我们还表明，量子化的边缘磁化可以导致自发亚铁磁秩序。
英文摘要：
The bulk electric polarization works as a nonlocal order parameter that characterizes topological quantum matters. Motivated by a recent paper [H. Watanabe \textit{et al.}, Phys. Rev. B {\bf 103}, 134430 (2021)], we discuss magnetic analogs of the bulk polarization in one-dimensional quantum spin systems, that is, quantized magnetizations on the edges of one-dimensional quantum spin systems.The edge magnetization shares the topological origin with the fractional edge state of the topological odd-spin Haldane phases. Despite this topological origin, the edge magnetization can also appear in topologically trivial quantum phases. We develop straightforward field theoretical arguments that explain the characteristic properties of the edge magnetization. The field theory shows that a U(1) spin-rotation symmetry and a site-centered or bond-centered inversion symmetry protect the quantization of the edge magnetization. We proceed to discussions that quantum phases on nonzero magnetization plateaus can also have the quantized edge magnetization that deviates from the magnetization density in bulk. We demonstrate that the quantized edge magnetization distinguishes two quantum phases on a magnetization plateau separated by a quantum critical point. The edge magnetization exhibits an abrupt stepwise change from zero to $1/2$ at the quantum critical point because the quantum phase transition occurs in the presence of the symmetries protecting the quantization of the edge magnetization. We also show that the quantized edge magnetization can result from the spontaneous ferrimagnetic order.
Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
本文讨论了轴对称均匀磁场中的零温量子自旋链。对于整数或半整数自旋，$S$，磁化曲线可以有平台，我们认为，每个网站$m$的磁化在平台上拓扑量化为$q (S - m)= integer$，其中$q$是基态的周期。我们还讨论了在这些量化值的高原的存在条件。对于$S=3/2$和$m=1/2$，我们研究了几种模型，并发现两种不同类型的大规模阶段的平台。其中之一被认为是半整数$S$的"Haldle间隙相“。
Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor
Texas Center for Superconductivity and Department of Physics, University of Houston（休斯顿大学物理系超导电性中心）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文学系）；Rice Center for Quantum Materials, Rice University（莱斯大学量子材料中心）
