The interaction fermion system under the periodic potential field is the core problem in quantum multibody theory and one of the fundamental problems in the study of condensed matter physics. The density functional theory (DFT) is an important theoretical framework to solve this core problem. Based on density functional theory, local density approximation (LDA) is the main theory and calculation method for quantitative research on solid energy bands. Since its introduction, it has been widely used in condensed matter physics and has achieved Great success. The basic acoustic, optical, electrical, and magnetic properties of most materials can be more accurately and quantitatively explained under the framework of DFT combined with LDA. The biggest feature of the theoretical framework of DFT + LDA is to avoid the perturbation expansion of the interaction strength, and instead to approximate the spatial non-uniformity of the Fermi system.
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