论文标题
一维哈伯德模型中的复兴和雷诺马隆
Resurgence and renormalons in the one-dimensional Hubbard model
论文作者
论文摘要
我们使用复兴分析来研究具有吸引人的相互作用和任意填充的一维，多组分哈伯德模型的非扰动方面。在两个组件的情况下，我们表明，地基态能量的扰动系列的主要borel奇异性是由能量差距确定的，这是超导系统的预期。事实证明，这种奇异性是肾上腺类型的，我们确定了一类导致正确阶乘生长的图表。由于我们的分析，我们提出了多组分哈伯德模型中弱耦合的能量差距的显式表达，在耦合常数中临时领先顺序。在两个组件的半填充情况下，我们使用Bethe Ansatz解决方案来确定基态能量的完整跨系列，以及其Stoks的确切形式不连续性。
We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is determined by the energy gap, as expected for superconducting systems. This singularity turns out to be of the renormalon type, and we identify a class of diagrams leading to the correct factorial growth. As a consequence of our analysis, we propose an explicit expression for the energy gap at weak coupling in the multi-component Hubbard model, at next-to-leading order in the coupling constant. In the two-component, half-filled case, we use the Bethe ansatz solution to determine the full trans-series for the ground state energy, and the exact form of its Stokes discontinuity.
