Abstract

We study the asymptotic decay of the Friedel density oscillations induced by an open boundary in a one-dimensional chain of lattice fermions with a short-range two-particle interaction. From Tomonaga-Luttinger liquid theory it is known that the decay follows a power law, with an interaction dependent exponent, which, for repulsive interactions, is larger than the noninteracting value − 1. We first investigate if this behavior can be captured by many-body perturbation theory for either the Green function or the self-energy in lowest order in the two-particle interaction. The analytic results of the former show a logarithmic divergence indicative of the power law. One might hope that the resummation of higher order terms inherent to the Dyson equation then leads to a power law in the perturbation theory for the self-energy. However, the numerical results do not support this. Next we use density functional theory within the local-density approximation and an exchange-correlation functional derived from the exact Bethe ansatz solution of the translational invariant model. While the numerical results are consistent with power-law scaling if systems of 10⁴ or more lattice sites are considered, the extracted exponent is very close to the noninteracting value even for sizeable interactions.

Graphical abstract

中文翻译：

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基于摄动理论和密度泛函理论的一维相关费米子的弗里德振荡

摘要

我们研究了一维费米子的一维链中具有短距离两粒子相互作用的，由开放边界引起的Friedel密度振荡的渐近衰减。从Tomonaga-Luttinger液体理论可知，衰变遵循幂定律，并且具有相互作用相关指数，对于排斥相互作用，该指数大于非相互作用值-1。我们首先研究这种行为是否可以被许多-人体微扰理论，即格林函数或两粒子相互作用中最低阶的自能。前者的分析结果显示出幂律的对数偏差。人们可能希望，戴森方程固有的高阶项的求和会导致自能量扰动理论中的幂定律。然而，数值结果不支持这一点。接下来，我们在局部密度近似中使用密度泛函理论，并从平移不变模型的精确Bethe ansatz解得到派生的交换相关函数。如果系统为10，则数值结果与幂律定标一致考虑到^4个或更多的晶格位点，即使对于较大的相互作用，提取的指数也非常接近非相互作用值。

图形概要