基于电离能理论的重整化群方法
Renormalization group method based on the ionization energy theory
摘要：
证明了电离能理论（IET）是一个重整化理论，它在数学上完全满足Gell-Mann-Low，Shankar和Zinn-Justin提出的重整化群形式.然而，IET的截止参数依赖于能级间距，而不是\textbf{k}空间中的晶格间距。随后，我们应用前面的证明，证明了电离能修饰的电子-电子屏蔽库仑势的数学结构与电离能修饰的电子-声子相互作用势的数学结构完全相同。后一个证明证明是通过二阶与时间无关的微扰理论与较重的有效质量的条件下，所需的电子-电子屏蔽库仑势。证明的结果是，我们可以导出热容和德拜频率作为电离能的函数，这可以应用于强关联物质和纳米结构。
英文摘要：
Proofs are developed to explicitly show that the ionization energy theory (IET) is a renormalized theory, which mathematically exactly satisfies the renormalization group formalisms developed by Gell-Mann-Low, Shankar and Zinn-Justin. However, the cutoff parameter for IET relies on the energy-level spacing, instead of lattice spacing in \textbf{k}-space. Subsequently, we apply the earlier proofs to prove that the mathematical structure of the ionization-energy dressed electron-electron screened Coulomb potential is exactly the same as the ionization-energy dressed electron-phonon interaction potential. The latter proof is proven by means of the second-order time-independent perturbation theory with the heavier effective mass condition, as required by the electron-electron screened Coulomb potential. The outcome of this proof is that we can derive the heat capacity and the Debye frequency as a function of ionization energy, which can be applied in strongly correlated matter and nanostructures.
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