Padé谱分解在强关联量子杂质体系理论研究中的应用

Strongly-correlated materials are a class of widely used electronic materials that show unusual electronic and magnetic properties. The behavior of their electrons cannot be described effectively by non-interacting models or simple mean field approximation theory. Theoretical models must include electronic correlation to be accurate. Therefore the simulations of strongly-correlated system dynamical properties and processes are extremely difficult. The most popular numerical methods include quantum Monte Carlo, density matrix renormalization group, and numerical renormalization group method, but they all have many limitations in application. Therefore, to develop a new accurate and efficient method for strongly-correlated system is an urgent need in condensed matter physics..　　Quantum hierarchical equations of motion is a quantum dissipation theory and is exactly equivalent to Feynman influence functional path integral method. It is non-perturbative and non-Markovian and it is suitable for research on strongly-correlated system. This project will develop a theory for strongly-correlated quantum impurity systems from Padé spectrum decomposition based hierarchical equations of motion method. We will use Anderson impurity model to study the spectral function of the single-impurity systems, the two-channel Kondo effect of the two-impurity systems, and extend to more general strongly-correlated models and will provide help to understand the unique nature of the strongly-correlated materials and to guide the experiments.

强关联材料是一类应用广泛的，具有非同寻常的电学和磁学性质的电子材料，其电子的行为不能用无相互作用模型，或简单的平均场近似理论来描述，而必须考虑电子-电子关联。因此，对强关联体系的动力学性质和过程的模拟极其困难。目前主流的数值方法包括量子蒙特卡洛方法、密度矩阵重整化群方法和数值重整化群方法，但这些方法在具体应用中都有很大的局限性。因此，适用于强关联体系的、准确高效的新方法的发展是凝聚态物理中一个亟待解决的重要问题。.　　量子耗散理论的量子级联运动方程方法是严格等价于费曼影响泛函路径积分方法的，是非微扰非马尔科夫的方法，它适用于强关联体系的研究。本项目将从基于Padé谱分解的量子级联运动方程方法来发展对强关联量子杂质体系的理论研究，以安德森杂质模型为示范，研究单杂质体系的谱函数，双杂质体系的双通道近藤效应，并且推广到其他强关联体系的特征理论计算研究，为理解材料的独特性质，指导实验提供帮助。

我们发展了一套基于Padé谱分解的量子级联运动方程数值方法来对强关联量子杂质体系的动力学性质做准确有效的模拟。这个方法可以定量地描述近藤效应和费米液体性质。以安德森单杂质模型为例，该方法在数值上能达到最新最近的数值重整化群方法的精确度。用该方法对安德森双杂质模型在变化的外场偏压下的微分电导进行研究，能准确的模拟两个杂质分别产生近藤效应到两个杂质形成自旋单态的连续性转变。级联运动方程方法在对量子杂质体系的平衡态和非平衡态的研究都非常出色，对于在动力学平均场框架下来研究强关联的晶格系统将有很大的优势。我们正在着手研究该方法对于其他耗散问题的应用，例如量子光学领域的问题等等。