Application of the real space decimation method in determining intricate electronic phases of matter: a review

The real space decimation method has been successfully applied over the years to understand the critical phenomena as well as the nature of single particle excitations in periodic, quasiperiodic, fractal, and decorated lattices in one dimension and beyond. The power of the method is specially revealed through its application in lattice models, leading to an elegant understanding of the nature of the single-particle states and the corresponding transport properties. In this review, we discuss, using a variety of decorated lattices, how the realm of this method is extended to unravel diverse electronic phases of matter, such as the Dirac systems, or lattices exhibiting flat bands and topological phase transitions.

Automated summary

The real space decimation method has been successfully used to study critical phenomena and single particle excitations in various types of lattices. It has provided elegant explanations for the nature of single-particle states and transport properties in lattice models. In this review, the application of this method in decorated lattices is discussed, showing how it can be used to uncover electronic phases such as Dirac systems, flat bands, and topological phase transitions.