Friedel oscillations of one-dimensional correlated fermions from perturbation theory and density functional theory
Friedel oscillations of one-dimensional correlated fermions from perturbation theory and density functional theory
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基于微扰理论和密度泛函理论的一维相关费米子的弗里德尔振荡
DOI：
10.1140/epjb/e2020-10127-1
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发表时间：
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通讯作者：
Volker Meden
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文献类型：
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作者：
Jovan Odavic;Nicole Helbig;Volker Meden
摘要研究了一维晶格费米子链中具有近程两粒子相互作用的开放边界诱导的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，具有相互作用依赖指数，对于排斥相互作用，该指数大于非相互作用值- 1。我们首先研究了这种行为是否可以用多体摄动理论来描述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幂律的对数散度。人们可能希望，戴森方程固有的高阶项的恢复会导致自能摄动理论中的幂律。然而，数值结果并不支持这一点。接下来，我们在局部密度近似中使用密度泛函理论和从平移不变模型的精确Bethe ansatz解中导出的交换相关泛函。当考虑104个或更多晶格点的系统时，数值结果与幂律缩放一致，即使对于相当大的相互作用，提取的指数也非常接近非相互作用值。图形抽象
AbstractWe 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 104or more lattice sites are considered, the extracted exponent is very close to the noninteracting value even for sizeable interactions.Graphical abstract