标题： 全息平均场理论中的拓扑结构在零温与有限温度情况下的研究 显示英文标题

标题： Topology in Holographic Mean-Field Theory at Zero and Finite Temperature

摘要： 我们研究在全息平均场理论（H-MFT）框架下强相互作用多体系统中的拓扑不变量。 在探测背景极限下，获得了所有可能费米子双线性相互作用的滞后格林函数的解析表达式$\mathrm{AdS}_4$，由此我们构建了拓扑哈密顿量。 对间隙谱在动量域上积分贝里曲率可得到明确且量子化的陈数，从而能够根据相互作用类型系统地对其进行分类。 这些拓扑不变量在相互作用和温度等变形参数下保持鲁棒，表明H-MFT在强关联系统中量子临界点附近编码了有效的单粒子态拓扑。 我们指出为什么在全息理论中定义了拓扑数，而在微扰场论中却没有。 显示英文摘要

摘要： We investigate topological invariants in strongly interacting many-body systems within holographic mean-field theory (H-MFT) framework. Analytic expressions for retarded Green's functions are obtained for all possible fermionic bilinear interactions in the limit of probe background limit $\mathrm{AdS}_4$, from which we construct topological Hamiltonians. Integrating Berry curvature over the momentum domain for the gapped spectra yields well-defined and quantized Chern numbers, enabling a systematic classification of them across interaction types. These topological invariants remain robust under deformation parameters like interaction and temperature, indicating that H-MFT encodes effective single-particle-state topology near a quantum critical point in strongly correlated systems. We point out why topological number is defined in the holographic theories while it is not in the perturbative field theory.