Institute for Mathematical Physics Product Vacua with Boundary States and the Classification of Gapped Phases Product Vacua with Boundary States and the Classification of Gapped Phases
Institute for Mathematical Physics Product Vacua with Boundary States and the Classification of Gapped Phases Product Vacua with Boundary States and the Classification of Gapped Phases
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数学物理研究所 具有边界态的积真空和带隙相的分类 具有边界态的积真空和带隙相的分类
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通讯作者：
B. Nachtergaele
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作者：
S. Bachmann;B. Nachtergaele
我们解决的问题，在一个维度上，不能区分的局部序参数的带隙基态的分类。我们在一维链上引入了一类量子自旋系统，它们在热力学极限下有一个独特的带隙基态，这是一个简单的乘积态，但在左半无限链和右半无限链上，它们有额外的零能量边缘态。这些模型被我们称为具有边界状态的积真空（PVBS），它形成的相位仅取决于与每个边界处的边缘状态数量相对应的两个整数。他们可以作为代表的等价类的这种间隙基态相位，我们展示了如何AKLT模型和SO（2J + 1）不变的概括适合这个分类。
We address the question of the classification of gapped ground states in one dimension that cannot be distinguished by a local order parameter. We introduce a family of quantum spin systems on the one-dimensional chain that have a unique gapped ground state in the thermody-namic limit that is a simple product state but which on the left and right half-infinite chains, have additional zero energy edge states. The models, which we call Product Vacua with Boundary States (PVBS), form phases that depend only on two integers corresponding to the number of edge states at each boundary. They can serve as representatives of equivalence classes of such gapped ground states phases and we show how the AKLT model and its SO(2J + 1)-invariant generalizations fit into this classification.