动态平均场论模拟与自适应采样组态相互作用方法
Dynamical Mean-Field Theory Simulations with the Adaptive Sampling Configuration Interaction Method
摘要：
为了精确描述强关联量子多体系统，动力学平均场论（DMFT）已经成为一种非常有用的工具，它可以用来解释物理现象模型和从头计算模型的光谱性质和量子相位。DMFT过程的关键是将原始系统自洽映射到Anderson杂质模型中，该模型的基态使用杂质求解器计算。因此，该方法的能力受到求解器可以处理的杂质模型的复杂性的限制。模拟现实系统通常需要许多相关的站点。通过调整最近提出的自适应采样配置相互作用（ASCI）方法作为杂质求解器，我们使更有效的零温度DMFT模拟。ASCI方法的关键特征是它只选择最相关的希尔伯特空间自由度来描述基态。这降低了计算的数值复杂性，这将使我们能够追求未来的DMFT模拟与更多的相关杂质网站比以前的作品。本文给出了ASCI-DMFT方法，并对一维和二维哈伯德模型进行了实例计算，证明了该方法的有效收敛性和时间特性。我们表明，ASCI方法是几个数量级的速度比目前最好的发表基态DMFT模拟，这使我们能够研究浴离散化误差模拟与小集群，以及解决集群的大小超出了目前的先进水平。我们的方法也可以适用于其他嵌入方法，如密度矩阵嵌入理论和自能嵌入理论。
英文摘要：
In the pursuit of accurate descriptions of strongly correlated quantum many-body systems, dynamical mean-field theory (DMFT) has been an invaluable tool for elucidating the spectral properties and quantum phases of both phenomenological models and ab initio descriptions of real materials. Key to the DMFT process is the self-consistent map of the original system into an Anderson impurity model, the ground state of which is computed using an impurity solver. The power of the method is thus limited by the complexity of the impurity model the solver can handle. Simulating realistic systems generally requires many correlated sites. By adapting the recently proposed adaptive sampling configuration interaction (ASCI) method as an impurity solver, we enable much more efficient zero temperature DMFT simulations. The key feature of the ASCI method is that it selects only the most relevant Hilbert space degrees of freedom to describe the ground state. This reduces the numerical complexity of the calculation, which will allow us to pursue future DMFT simulations with more correlated impurity sites than in previous works. Here we present the ASCI-DMFT method and example calculations on the one-dimensional and two-dimensional Hubbard models that exemplify its efficient convergence and timing properties. We show that the ASCI approach is several orders of magnitude faster than the current best published ground state DMFT simulations, which allows us to study the bath discretization error in simulations with small clusters, as well as to address cluster sizes beyond the current state of the art. Our approach can also be adapted for other embedding methods such as density matrix embedding theory and self-energy embedding theory.
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