基于自然轨道重整化群的团簇动力学平均场理论

项目名称： 基于自然轨道重整化群的团簇动力学平均场理论

项目编号： No.11474356

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 卢仲毅

作者单位： 中国人民大学

项目金额： 85万元

中文摘要： 团簇动力学平均场理论是一个研究关联电子系统的强有力的方法，目前阻碍其进一步发展的核心问题是如何发展出一个高效求解多自由度相互作用的量子杂质模型的方法。另一方面，量子重整化群方法则是研究相互作用多电子关联系统最重要最精确的方法之一，数值计算上它主要包含数值重整化群和密度矩阵重整化群。前者适合处理量子杂质模型，但所含杂质自由度不能多于两个；而后者则适合于处理一维系统。最近我们提出自然轨道重整化群方法，它是量子重整化群在被推广到实空间的密度矩阵重整化群后，又一个重要的推广，即是推广到一般的抽象轨道空间的重整化群。该新方法不仅可以求解量子多杂质多轨道模型的基态或目标态，同时也能给出相应的低能物理性质，因而该方法不仅仅为团簇动力学平均场理论的发展提供了一个全新的优质杂质求解器的可能，而且也直接为处理多杂质的Kondo问题和轨道物理以及重费米子系统等提供实质性的帮助。本申请书计划在此方面展开研究。

中文关键词： 强关联电子体系；电子结构计算；量子相变；近藤效应；重费米子

英文摘要： The cluster dynamical mean field theory (CDMFT) is a powerful approach to deal with correlated electron systems. Currently the core difficulty for further developing the CDMFT is how to construct a highly efficient impurity solver for a quantum impurity model with multi-interacting degrees. On the other hand, the quantum renormalization group (RG) procedure is one of the most important and accurate approaches for studying interacting many-electron correlated systems. The RG approaches include numerical RG (NRG) and density matrix RG (DMRG) methods. The NRG works only on quantum impurity problems with impurities/orbitals no more than two, while the DMRG works basically in one-dimensional (1D) systems. Recently we proposed the natural orbitals renormalization group approach, which is a generalization of the RG into general orbital space after the DMRG as a generalization of the RG from energy space into real space. The new approach is naturally appropriate for studying not only the ground/targeted state but also the low-energy properties of a quantum impurity model with multi-interacting degrees. Therefore it will provide invaluable help in not only the construction of a highly efficient impurity solver for the cluster dynamical mean-field theory, but also studying of multi-impurity/orbital Kondo problems and heavy fermion systems. We plot a detailed research plan along this direction in this application.

英文关键词： strongly correlated electronic systems;electronic structure calculations;quantum phase transitions;Kondo effect;heavy fermions