格林函数运动方程方法是凝聚态理论中处理量子多体问题的传统方法之一，具有理论简单和普适的优点。然而，在应用中，传统的运动方程方法存在截断近似的任意性和结果精度不可控等缺点，严重限制了其在现代凝聚态物理研究中的应用。本项目基于申请人的近期工作，提出基于算符投影方法实现格林函数运动方程的数值化。拟给出一种能够继承传统格林函数运动方程方法优点并消除其缺点的新型计算方法，对给定量子多体模型给出精度可控、与主流计算方法精度相当的数值结果，但具有更大的普适性。其基本思路为：采用算符投影技术和矩阵化Mori-Zwanzig理论框架，在选定的算符子空间内将运动方程转化为矩阵代数问题进行数值求解；对涉及到的算符平均值进行自洽计算；以及用计算机实现算符对易子的自动计算。在本申请书中，我们详细阐述了该项目的研究背景和立项依据，描述了具体的研究内容、拟采用的技术路线、所需解决的关键科学问题，以及项目可行性。

The equation of motion approach to Green's function is one of the traditional theoretical methods for quantum many-body problems in condensed matter physics. It has the merit of simplicity and universality. However, its application in practice is hampered by its shortcomings: the arbitrariness in the decoupling truncation approximation and the poor controlability of precision in results. Based on the recent work of the applicant, we propose to computerize the equation of motion of Green's function calculation based on the operator projection method. This can produce a new computational method which inherits the merit of traditional equation of motion method while removes its shortcomings. It can provide results with precision controlable and comparable to the other main stream methods, but it has wider applicability. The basic strategy is: transforming the equation of motion calculation into a matrix algebraic problem using the operator projection and the matrix Mori-Zwanzig theory; solving the matrix problem numerically; carring out self-consistent calculation for the averages of operators; and implementing the automatic calculation of operator commutators on a computer. In this proposal, we present the background of this project and the justification of our proposal, with detailed description of the research content, technical strategy, the key scientific problem, and the feasibility.