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Structural Chemistry

About the concept of electron localization

Sebastián Fortín, Olímpia Lombardi

Published Aug 18, 2025• 1 citation
Publisher
DOI
10.1007/s11224-025-02587-3

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Abstract We have seen that disordered systems give rise to a host of interesting effects related to the localization of states. Thus, from the outset we have explicitly to take account of the localization in the theoretical framework, which makes computer experiments on finite systems an important first-principles method. This situation immediately poses several essential questions, such as: (i) how can the properties of macroscopic systems be deduced from the results for finite systems; and (ii) how can the concept of Anderson localization be extended to disordered systems with electron-electron interactions in a numerical model in which disorder and electron correlation are treated on an equal footing? In this chapter we address these questions. In this section we introduce the concept of renormalization for disordered systems. Specifically, we examine real-space renormalization schemes.
The universal nature and limitations of the local field concept in the modem theory of systems of interacting fermions is considered. A generalization of this concept based on the construction of a set of functions including the local field correction and its variational derivatives is proposed. Integral equations for these functions are obtained, and the existence of their solutions for a Fermi system with a positive Fourier transform of the two-particle interaction potential is proved. The results of calculation of the local field correction and residual Fermi surface at absolute zero temperature in the electron liquid model are presented.