Kitaev阿贝尔量子偶模型的无限体积基态完备集
The complete set of infinite volume ground states for Kitaev's abelian quantum double models
摘要：
研究了任意有限交换群$G$的$\mathbb{Z}^2$上Kitaev量子双模型的无限体积基态集.已知这些模型具有独特的无阻挫基态。在这里，我们放弃了无阻挫的要求，并对完整的基态进行了分类。我们表明，基态空间分解成$|G|^2$不同的带电扇区，对应于不同类型的阿贝尔任意子（也称为超选择扇区）。特别地，所有纯基态都等价于可以被解释为描述单个激发的基态。我们的证明表明，每个基态可以得到的弱$^*$极限的有限体积基态的量子双模型与适当的边界条件。边界项允许表示一对激发的状态，其中一个激发在体中，一个被钉扎到边界，被包括在基态空间中。
英文摘要：
We study the set of infinite volume ground states of Kitaev's quantum double model on $\mathbb{Z}^2$ for an arbitrary finite abelian group $G$. It is known that these models have a unique frustration-free ground state. Here we drop the requirement of frustration freeness, and classify the full set of ground states. We show that the ground state space decomposes into $|G|^2$ different charged sectors, corresponding to the different types of abelian anyons (also known as superselection sectors). In particular, all pure ground states are equivalent to ground states that can be interpreted as describing a single excitation. Our proof proceeds by showing that each ground state can be obtained as the weak$^*$ limit of finite volume ground states of the quantum double model with suitable boundary terms. The boundary terms allow for states which represent a pair of excitations, with one excitation in the bulk and one pinned to the boundary, to be included in the ground state space.
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