The Kitaev honeycomb model has attracted significant attention due to its exactly solvable spin-liquid ground state with fractionalized Majorana excitations and its possible materialization in magnetic Mott insulators with strong spin-orbit couplings. Recently, the $5d$-electron compound ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ has shown to be a strong candidate for Kitaev physics considering the absence of any signs of a long-range ordered magnetic state. In this work, we demonstrate that a finite density of random vacancies in the Kitaev model gives rise to a striking pileup of low-energy Majorana eigenmodes and reproduces the apparent power-law upturn in the specific heat measurements of ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$. Physically, the vacancies can originate from various sources such as missing magnetic moments or the presence of nonmagnetic impurities (true vacancies), or from local weak couplings of magnetic moments due to strong but rare bond randomness (quasivacancies). We show numerically that the vacancy effect is readily detectable even at low vacancy concentrations and that it is not very sensitive either to the nature of vacancies or to different flux backgrounds. We also study the response of the site-diluted Kitaev spin liquid to the three-spin interaction term, which breaks time-reversal symmetry and imitates an external magnetic field. We propose a field-induced flux-sector transition where the ground state becomes flux-free for larger fields, resulting in a clear suppression of the low-temperature specific heat. Finally, we discuss the effect of dangling Majorana fermions in the case of true vacancies and show that their coupling to an applied magnetic field via the Zeeman interaction can also account for the scaling behavior in the high-field limit observed in ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$.

中文翻译：

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Kitaev自旋液体中空位引起的低能态密度

Kitaev蜂窝模型由于具有精确的自旋液体基态和分数阶的Majorana激发，并且在具有强自旋轨道耦合的磁性Mott绝缘子中可能物化，因此引起了广泛的关注。最近，$5d$电子化合物 ${\mathrm{H}}_3{I}_2{\mathrm{Ø}}_6$考虑到不存在任何长程有序磁态的迹象，他已被证明是Kitaev物理学的强力候选人。在这项工作中，我们证明了Kitaev模型中随机空位的有限密度引起了低能量的Majorana本征模的惊人堆积，并再现了比热测量中的表观幂律上扬。${\mathrm{H}}_3{I}_2{\mathrm{Ø}}_6$。从物理上讲，空位可能来自各种来源，例如磁矩缺失或非磁性杂质的存在（真实空位），也可能是由于强但稀有的键随机性（准分子性）导致的磁矩局部弱耦合。我们从数字上显示出，即使在低空位浓度下，空位效应也很容易检测到，并且它对空位的性质或对不同通量背景不是很敏感。我们还研究了现场稀释的Kitaev自旋液体对三自旋相互作用项的响应，这打破了时间反转对称性并模仿了外部磁场。我们提出了一种磁场感应的磁通扇形过渡，其中大面积磁场的基态变为无磁通，从而明显抑制了低温比热。最后，${\mathrm{H}}_3{I}_2{\mathrm{Ø}}_6$。