Kosterlitz-numerless相位和$Z_d$拓扑量子相位
Kosterlitz-Thouless phase and $Z_d$ topological quantum phase
摘要：
已经知道，将经典自旋模型的玻尔兹曼权重编码在多体波函数的振幅中可以提供其相位结构通过使用经典相变来表征的量子模型。特别是，这样的对应关系可以导致找到新的量子相位对应于众所周知的经典相位。在这里，我们调查这个问题的Kosterlitz无（KT）阶段的d-状态时钟模型，我们发现一个相应的量子模型构造通过应用局部可逆变换的d-水平版本的Kitaev的Toric代码。特别地，我们证明了这种量子模型中的基态保真度映射到时钟模型的热容。因此，我们确定了一个扩展的拓扑相变在我们的模型在某种意义上说，对于$d \geq 5$，KT类量子相位之间出现的$Z_d$拓扑阶段和平凡阶段。然后，使用一个映射到时钟模型中的关联函数，我们引入了一个非本地（字符串）的量子模型的观察，指数衰减的两个端点之间的距离相应的字符串在$Z_d$拓扑阶段，而它显示了一个幂律的行为在KT类阶段。最后，利用已知的d态时钟模型的转变温度，我们给出了证据，证明了当d增大时，$Z_d$拓扑相和类KT相的稳定性都增大，但当d增大时，类KT相甚至比$Z_d$拓扑相更稳定.
英文摘要：
It has been known that encoding Boltzmann weights of a classical spin model in amplitudes of a many-body wave function can provide quantum models whose phase structure is characterized by using classical phase transitions. In particular, such correspondence can lead to find new quantum phases corresponding to well-known classical phases. Here, we investigate this problem for Kosterlitz-Thouless (KT) phase in the d-state clock model where we find a corresponding quantum model constructed by applying a local invertible transformation on a d-level version of Kitaev's Toric code. In particular, we show the ground state fidelity in such quantum model is mapped to the heat capacity of the clock model. Accordingly, we identify an extended topological phase transition in our model in a sense that, for $d \geq 5$, a KT-like quantum phase emerges between a $Z_d$ topological phase and a trivial phase. Then, using a mapping to the correlation function in the clock model, we introduce a non-local (string) observable for the quantum model which exponentially decays in terms of distance between two endpoints of the corresponding string in the $Z_d$ topological phase while it shows a power law behavior in the KT-like phase. Finally, using well-known transition temperatures for d-state clock model we give evidences to show that while stability of both $Z_d$ topological phase and the KT-like phase increases by increasing d, the KT-like phase is even more stable than the $Z_d$ topological phase for large d.
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