论文标题
热力学多体扰动理论的低温分解
Low-temperature breakdown of many-body perturbation theory for thermodynamics
论文作者
论文摘要
从分析和数值上显示，大规范合奏中有限的多体扰动理论在零温度下的收敛性零半径在零温度下，当基态的能量排序或退化程度随扰动强度而变化。当参考状态的退化是在一阶Hirschfelder-caunter-cautional-clenter扰动理论中部分或完全提升的时，巨大的电位和内部能量分歧为$ t \ to 0 $。与早期对化学潜力$μ$的可恢复性的建议相反，这种非结合性是由W. Kohn和J. M. Luttinger首先怀疑的，是由Boltzmann因子$ e^{ - e/k_ \ e/k_ \ e/k_ \ text {b} t} $ t = 0 $ t = 0 $的非分析性质引起的。该发现揭示了扰动理论中的基本缺陷，该缺陷深深植根于电力系列扩展的数学局限性，不太可能在其框架内消除。
It is shown analytically and numerically that the finite-temperature many-body perturbation theory in the grand canonical ensemble has zero radius of convergence at zero temperature when the energy ordering or degree of degeneracy for the ground state changes with the perturbation strength. When the degeneracy of the reference state is partially or fully lifted at the first-order Hirschfelder-Certain degenerate perturbation theory, the grand potential and internal energy diverge as $T \to 0$. Contrary to earlier suggestions of renormalizability by the chemical potential $μ$, this nonconvergence, first suspected by W. Kohn and J. M. Luttinger, is caused by the nonanalytic nature of the Boltzmann factor $e^{-E/k_\text{B}T}$ at $T=0$, also plaguing the canonical ensemble, which does not involve $μ$. The finding reveals a fundamental flaw in perturbation theory, which is deeply rooted in the mathematical limitation of power-series expansions and is unlikely to be removed within its framework.
