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arXiv 2201.01472cond-mat.str-elcond-mat.dis-nncond-mat.quant-gas
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非掺杂石墨烯中电子-声子相互作用和库仑相互作用的非微扰研究

A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene

Zhao-Kun Yang, Xiao-Yin Pan, Guo-Zhu Liu

摘要:

在凝聚态系统中,电子在一定条件下会受到两种不同的相互作用。即使两种相互作用都很弱,由于两种相互作用的相互作用所引起的复杂性,也很难进行微扰计算。当一个或两个相互作用很强时,普通的微扰理论就可能失效。在这里,我们考虑未掺杂的石墨烯作为一个例子,并提供一个非微扰的量子场论分析的相互作用的电子-声子相互作用和库仑相互作用。我们把这两个相互作用在一个平等的基础上,并推导出完整的狄拉克-费米子传播子的确切戴森-Schwinger积分方程。该方程依赖于几个复杂的关联函数,因此难以处理。幸运的是,我们发现这些关联函数服从一些精确的恒等式,这使我们能够证明全费米子传播子的Dyson-Schwinger方程是自封闭的。在求解了这个自封闭方程后,我们得到了狄拉克费米子的重整化速度,并指出它的能量(动量)依赖性主要取决于电子-声子(库仑)相互作用.特别地,重整化速度表现出对数动量依赖性和非单调能量依赖性。

英文摘要:

In condensed-matter systems, electrons are subjected to two different interactions under certain conditions. Even if both interactions are weak, it is difficult to perform perturbative calculations due to the complexity caused by the interplay of two interactions. When one or two interactions are strong, ordinary perturbation theory may become invalid. Here we consider undoped graphene as an example and provide a non-perturbative quantum-field-theoretic analysis of the interplay of electron-phonon interaction and Coulomb interaction. We treat these two interactions on an equal footing and derive the exact Dyson-Schwinger integral equation of the full Dirac-fermion propagator. This equation depends on several complicated correlation functions and thus is difficult to handle. Fortunately, we find that these correlation functions obey a number of exact identities, which allows us to prove that the Dyson-Schwinger equation of the full fermion propagator is self-closed. After solving this self-closed equation, we obtain the renormalized velocity of Dirac fermions and show that its energy (momentum) dependence is dominantly determined by the electron-phonon (Coulomb) interaction. In particular, the renormalized velocity exhibits a logarithmic momentum dependence and a non-monotonic energy dependence.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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