报告题目：Algebraic-Dynamical Theory for Quantum Many-body Hamiltonians: A Formalized Approach To Strongly Interacting Systems
报 告 人：丁文新 教授 （安徽大学）
报告时间：2022年1月10日（星期一）上午10:30
报告地点：物理学院LE201
邀 请 人：胡自翔
报告人简介：
丁文新博士2006年本科毕业于浙江大学物理系，2012年于美国佛罗里达州立大学与美国强磁场国家实验室获得博士学位，之后先后在莱斯大学，加州大学圣克鲁兹分校以及中国科学院大学卡弗里理论科学研究所从事博士后研究。2017年起受聘安徽大学物理与材料科学学院教授。他的主要从事强关联电子系统基础理论研究，研究兴趣包括铜氧化物超导体，重费米子材料，量子纠缠，阻挫量子磁性体系等，着重关注上述体系的微观模型的方法论的研究。
报告摘要：
In this work, we formulate a {\it algebraic-dynamical theory} (ADT) by combining the full power of both the quantum algebras and the dynamical methods. In ADT, we introduce a {\it complete operator basis set} (COBS). Then, an arbitrary state, either pure or mixed, can be represented by the expectation values of COBS. ADT establishes a complete mapping from an arbitrary state to a complete set of dynamical correlation functions through the Heisenberg- and Schwinger-Dyson-equations-of-motion (SDEOM). Such construction ensures ADT to be a mathematically {\it complete} theory in principle. Applying ADT to many-body systems on lattices, we find that the quantum entanglement, which is can be characterized as a hierarchical structure in correlations, is represented by a cumulant structure in the expectation values of COBS. More importantly, such static correlational hierarchy is {\it inherited} by the dynamical correlations and their SDEOM. We propose that the dynamical hierarchy will be manifesto in perturbation theories, i.e. perturbation needs to start with the correlation functions at the top of the hierarchy. We demonstrate the validity of such perturbation hierarchy with an explicit example, in which we show that a single particle perturbative calculation fails while a many-body perturbation following the hierarchy succeeds. We also discuss the computation and approximation schemes of ADT and its implications to other strong coupling theories like parton methods and slave particle methods.
