In this study, we addressed the influence of quantum singularity on the topological state. The quantum singularity creates the defect in the momentum space ubiquitously and leads to the phase transition for the topological material. The kinetic equation reveals that the defect generates an anomaly without the characteristic energy scale. In the holographic model, the three-dimensional dislocations map into the gravitational bulk as domain walls extending along the AdS radial direction from the boundary. The creation/annihilation of the domain wall causes the quantum phase transition by ’t Hooft anomaly generation and is controlled by the gauge field. In other words, the phase transition is realized by the anomaly inflow. This ’t Hooft anomaly is caused by a phase ambiguity of the ground state resulting from the singularity in parameter space. This singularity gives the basis for the boundary’s topological state with the Berry connection. ’t Hooft anomaly’s renormalization group invariance shows that the total Berry flux is conserved in the UV layer to the IR layer. Phase transition entails domain wall constitution, which generates the entropy from the non-universal form or quantum entropy correction.

中文翻译：

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全息量子奇点

在这项研究中，我们解决了量子奇点对拓扑状态的影响。量子奇点在动量空间中无处不在地产生缺陷，并导致拓扑材料的相变。动力学方程表明，缺陷产生了没有特征能量标度的异常。在全息模型中，三维位错映射到重力体中，作为畴壁从边界沿 AdS 径向方向延伸。畴壁的产生/湮灭通过't Hooft异常产生引起量子相变，并由规范场控制。换言之，相变是通过异常流入来实现的。这种 't Hooft 异常是由参数空间中的奇异性导致的基态相位模糊引起的。这种奇点为边界与 Berry 连接的拓扑状态提供了基础。't Hooft 异常的重整化群不变性表明总的 Berry 通量在 UV 层到 IR 层是守恒的。相变需要畴壁构成，它从非通用形式或量子熵校正产生熵。