Quantum Monte Carlo impurity solvers for multi-orbital problems and frequency-dependent interactions

用于多轨道问题和频率相关相互作用的量子蒙特卡罗杂质求解器

• 批准号: 175386010
• 负责人: Professor Dr. Fakher Fakhry Assaad, since 7/2015
• 金额: --
• 依托单位: Department of Physics
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/175386010?language=en
• 关键词: Quantum; Monte; Carlo; impurity; solvers

Modern methods to describe and predict properties of materials with strong electronic correlations rely on a combination of density functional and dynamical mean-field theories. This approach reduces a fermionic lattice problem to the self-consistent solution of a quantum impurity model and, thus, relies on efficient methods to solve impurity problems. These so-called impurity solvers constitute the core of this research project. In recent years, we have witnessed breakthroughs in this domain with the development of continuous time (diagrammatic) quantum Monte Carlo approaches as well as a multigrid formulation of the well-known Hirsch-Fye algorithm. The diagrammatic Monte Carlo methods can be applied to multiorbital systems with the full rotationally invariant Coulomb interactions and, thus, appear suitable for the study of transition metal and actinide compounds. One purpose of this project is to compare the performance of the different Monte Carlo approaches, to establish the parameter regimes in which they work most efficiently, and to study the effect of previously neglected interactions. The second purpose is to extend the continuous-time impurity solvers to frequency-dependent (screened) interactions, which are expected to be relevant for a quantitative description of some transition metal compounds.

描述和预测具有强电子相关性的材料性质的现代方法依赖于密度泛函理论和动态平均场理论的结合。该方法将费米子晶格问题简化为量子杂质模型的自洽解，从而依赖于有效的方法来解决杂质问题。这些所谓的杂质解决剂构成了这个研究项目的核心。近年来，随着连续时间（图解）量子蒙特卡罗方法的发展以及著名的Hirsch-Fye算法的多网格公式的发展，我们见证了这一领域的突破。图解蒙特卡罗方法可以应用于具有完全旋转不变库仑相互作用的多轨道系统，因此，似乎适合于过渡金属和锕系化合物的研究。该项目的目的之一是比较不同蒙特卡罗方法的性能，建立它们最有效工作的参数制度，并研究以前被忽视的相互作用的影响。第二个目的是将连续时间杂质解算器扩展到频率依赖（筛选）的相互作用，这有望与一些过渡金属化合物的定量描述相关。