Real Space Renormalization Group Techniques and Applications

TL;DR

This paper reviews Real Space Renormalization Group techniques, especially DMRG, highlighting their theoretical basis and applications in quantum mechanics, partial differential equations, and complex media, serving as an educational overview.

Contribution

It provides a comprehensive, pedagogical review of RSRG methods and their successful applications, emphasizing the theoretical understanding behind their effectiveness.

Findings

Successful application of DMRG to quantum systems

Analysis of spectra in dendrimers and random media

Theoretical insights into RSRG techniques

Abstract

Real Space Renormalization Group (RSRG) techniques and their applications, mainly to quantum mechanics and to partial differential equations, are discussed. Special emphasis is given to the theoretical insight and the reasons for the success of some techniques, specially DMRG. Applications to the spectrum of dendrimers and excitons on random media are considered. This work is the Ph.D. of the author. Almost all the results have already been published. The main interest of this text is paedagogical and as a review.