In this paper, we investigate a feasible holography with the Kitaev model using dilatonic gravity in AdS₂. We propose a generic dual theory of gravity in the AdS₂ and suggest that this bulk action is a suitable toy model in studying quantum mechanics in Kitaev model using gauge/gravity duality. This gives a possible equivalent description for the Kitaev model in the dual gravity bulk. Scalar and tensor perturbations are investigated in details. In the case of near AdS perturbation, we show that the geometry still “freezes” as is AdS, while the dilation perturbation decays at the AdS boundary safely. The time-dependent part of the perturbation is an oscillatory model. We discover that the dual gravity induces an effective and renormalizable quantum action. The entanglement entropy for bulk theory is computed using extremal surfaces. We prove that these surfaces have a fold bifurcation regime of criticality.

中文翻译：

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一维Kitaev格子模型的折叠分岔纠缠面

_{在本文中，我们使用 AdS 2}中的膨胀引力研究了一种可行的全息术，它采用 Kitaev 模型。_{我们在 AdS 2}中提出了一个通用的对偶引力理论并建议在使用规范/重力对偶的 Kitaev 模型中研究量子力学时，这种体积作用是一个合适的玩具模型。这为双重力体中的 Kitaev 模型提供了可能的等效描述。详细研究了标量和张量扰动。在接近 AdS 扰动的情况下，我们表明几何仍然像 AdS 一样“冻结”，而膨胀扰动在 AdS 边界处安全地衰减。扰动的时间相关部分是一个振荡模型。我们发现双重引力引发了有效且可重整的量子作用。体积理论的纠缠熵是使用极值表面计算的。我们证明这些表面具有临界的折叠分岔机制。