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Symmetry-protected topological order in magnetization plateau states of quantum spin chains

机译：量子自旋链磁化稳定态的对称保护拓扑顺序

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摘要

A symmetry-protected topologically ordered phase is a short-range entangled state, for which some imposed symmetry prohibits the adiabatic deformation into a trivial state which lacks entanglement. In this paper we argue that magnetization plateau states of one-dimensional antiferromagnets which satisfy the conditions S - m ∈ odd integer, where S is the spin quantum number and m the magnetization per site, can be identified as symmetry-protected topological states if an inversion symmetry about the link center is present. This assertion is reached by mapping the antiferromagnet into a nonlinear sigma model type effective field theory containing a novel Berry phase term (a total derivative term) with a coefficient proportional to the quantity S - m, and then analyzing the topological structure of the ground state wave functional which is inherited from the latter term. A boson-vortex duality transformation is employed to examine the topological stability of the ground state in the absence/presence of a perturbation violating link-center inversion symmetry. Our prediction based on field theories is verified by means of a numerical study of the entanglement spectra of actual spin chains, which we find to exhibit twofold degeneracies when the aforementioned condition is met. We complete this study with a rigorous analysis using matrix product states.
机译：对称保护的拓扑有序相是短程纠缠态，为此，某些强加的对称性阻止了绝热变形成没有纠缠的琐碎状态。在本文中，我们认为满足条件S-m∈奇数整数（其中S为自旋量子数，m为每个位置的磁化强度）的一维反铁磁体的磁化平稳态可以被识别为对称保护的拓扑态。存在关于链接中心的反对称性。通过将反铁磁体映射到非线性sigma模型类型的有效场论中可以得出这一结论，该理论包含一个新颖的Berry相项（一个总导数项），其系数与数量S-m成正比，然后分析基态的拓扑结构波函数是从后一项继承而来的。玻色子-涡旋对偶变换用于检查在不存在/存在违反链接中心反转对称性的扰动的情况下基态的拓扑稳定性。通过对实际自旋链的纠缠谱进行数值研究，验证了我们基于场论的预测，当满足上述条件时，我们发现其表现出双重简并性。我们使用矩阵乘积状态进行了严格的分析，从而完成了本研究。

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