AI 中文总结
该研究针对拓扑系统中轨道磁化率计算失效问题，建立有限磁场HF问题的代数框架，经计算证实扭曲MoTe₂陈绝缘体中相互作用可反转轨道磁化率符号。
AI 中文摘要
已充分证实，相互作用电子的轨道磁化可通过将单粒子公式应用于自洽HF（哈特里-福克）带进行简单计算。然而，我们表明该过程对轨道磁化率而言存在定性失效，尤其在拓扑系统中：在扭曲MoTe₂的陈绝缘相里，相互作用诱导的修正会反转磁化率的符号。该结果源于求解有限磁场下HF问题的代数框架，其中非对易正则动量阻碍了直接计算：一种“反向佩尔斯替换”将所有磁平移不变算子映射为唯一的二元函数，把有限场自洽性转化为可在B（磁场）中系统展开的函数方程。一阶近似下，这给出了Fock势场诱导变化δX的线性方程，除类单粒子磁化率外，还产生了本质上由相互作用诱导的磁化率。该框架重现了绝缘体的Středa公式，辅助希尔伯特空间构造可将其推广至周期与莫尔系统。对带隙狄拉克模型及扭曲MoTe₂陈绝缘体的有限场HF计算，定量证实了该理论。
英文摘要
It has been well established that the orbital magnetization of interacting electrons can be simply evaluated by applying the single-particle formula to self-consistent HF bands. However, we show that such procedure fails qualitatively for orbital magnetic susceptibility, especially in topological systems: in a Chern-insulating phase of twisted MoTe$_2$, the interaction-induced correction reverses the sign of the susceptibility. This result follows from an algebraic framework that solves the HF problem at finite magnetic field, where noncommuting canonical momenta obstruct a direct calculation: a \emph{reverse Peierls substitution} maps every magnetic-translation-invariant operator to a unique bivariate function, converting the finite-field self-consistency into a function equation that can be expanded systematically in $B$. At first order, this yields a linear equation for the field-induced change $δX$ of the Fock potential, leading to an intrinsically interaction-induced susceptibility in addition to a single-particle-like one. The framework reproduces the Středa formula for insulators, and an auxiliary-Hilbert-space construction carries it to periodic and moiré systems. Finite-field HF calculations in a gapped Dirac model and in the twisted-MoTe$_2$ Chern insulator confirm the theory quantitatively.
Comments8 pages, 2 figures. Comments are welcome
