变分离散Action理论
Variational Discrete Action Theory
摘要：
本文提出用变分离散作用量理论研究量子多体哈密顿量的基态性质。VDAT是一种基于序贯乘积密度矩阵（SPD）的变分理论，其特征是一个整数$\mathcal{N}$，随着$\mathcal{N}$的增加，它单调地逼近精确解.为了评估SPD，我们引入了一个离散的行动和相应的整数时间格林函数。本文用VDAT精确地计算了两种典型的电子相互作用模型：安德森杂质模型（AIM）和$d=\infty$哈伯德模型中的SPD。对于后者，我们评估$\mathcal{N}=2-4$，其中$\mathcal{N}=2$恢复的Gutzwiller近似（GA），我们表明，$\mathcal{N}=3$，这正是评估的Gutzwiller-Baeriswyl波函数，提供了一个真正的最小但精确的描述莫特物理与成本类似的GA。VDAT是一种灵活的理论，用于研究量子哈密顿，在一个框架内与最先进的方法和简单有效的方法竞争。
英文摘要：
Here we propose the Variational Discrete Action Theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer $\mathcal{N}$, which monotonically approaches the exact solution with increasing $\mathcal{N}$. To evaluate the SPD, we introduce a discrete action and a corresponding integer time Green's function. We use VDAT to exactly evaluate the SPD in two canonical models of interacting electrons: the Anderson impurity model (AIM) and the $d=\infty$ Hubbard model. For the latter, we evaluate $\mathcal{N}=2-4$, where $\mathcal{N}=2$ recovers the Gutzwiller approximation (GA), and we show that $\mathcal{N}=3$, which exactly evaluates the Gutzwiller-Baeriswyl wave function, provides a truly minimal yet precise description of Mott physics with a cost similar to the GA. VDAT is a flexible theory for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework.
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