We study linear responses to metric perturbation in two-dimensional topological systems based on the Dirac fermion formalism. We introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT correspondence. This quantity corresponds to the filling fraction which characterizes the quantum Hall states, and hence it could be discussed in Haldane’s zero-field quantum Hall system. We also consider dissipationless viscosity in the time reversal invariant quantum spin Hall system, which is a spin analog of the Hall viscosity.

中文翻译：

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二维拓扑系统中的霍尔和自旋霍尔粘度

我们研究基于狄拉克费米子形式主义的二维拓扑系统中度量摄动的线性响应。我们介绍了一个新的量，霍尔粘度与颗粒密度之比，类似于AdS / CFT对应关系所建议的粘度与熵之比。该量对应于表征量子霍尔态的填充分数，因此可以在霍尔丹的零场量子霍尔系统中进行讨论。我们还考虑了时间反向不变量子自旋霍尔系统中的无耗散粘度，这是霍尔粘度的自旋类似物。