The Correlated Block Renormalization Group

TL;DR

This paper introduces a correlated block renormalization group method that accounts for inter-block correlations dynamically, improving the analysis of lattice models like the 1D and 2D tight-binding models.

Contribution

It presents a novel real-space renormalization group approach incorporating correlations between blocks through dynamical operators, enhancing traditional methods.

Findings

Effective in 1D and 2D tight-binding models

Handles various boundary conditions

Improves accuracy over uncorrelated RG methods

Abstract

We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of its neighbours. We illustrate our method in the example of the tight-binding model in 1D and 2D for various types of boundary conditions.