We compute the quantum Fisher information (QFI) associated with two different local operators in the ground state of the Kitaev honeycomb model, and find divergent behavior in the second derivatives of these quantities with respect to the driving parameter at the quantum phase transition between the gapped and gapless phases for both fully antiferromagnetic and fully ferromagnetic exchange couplings, thus demonstrating that the second derivative a locally defined, experimentally accessible, QFI can detect topological quantum phase transitions. The QFI associated with a local magnetization operator behaves differently from that associated with a local bond operator depending on whether the critical point is approached from the gapped or gapless side. We show how the behavior of the second derivative of the QFI at the critical point can be understood in terms of the diverging length scales associated to the two and four point correlators of the Majorana degrees of freedom. We present critical exponents associated with the divergences of these length scales.

中文翻译：

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在Kitaev蜂窝模型中使用量子Fisher信息揭示发散的长度尺度

我们在基塔耶夫蜂窝模型的基态中计算与两个不同的本地算子相关的量子费舍尔信息（QFI），并在间隙之间的量子相变处相对于驱动参数，发现这些量的二阶导数的发散行为。完全反铁磁和完全铁磁交换耦合的无间隙相，因此证明了二阶导数是局部定义的，实验可访问的QFI可以检测拓扑量子相变。与局部磁化算符关联的QFI的行为与与局部键合算符关联的QFI的行为不同，这取决于是从间隙侧还是无间隙侧逼近临界点。我们展示了如何根据与马约拉那自由度的两点和四点相关器相关的发散长度尺度来理解QFI在临界点的二阶导数的行为。我们提出了与这些长度尺度的差异相关的关键指数。