Real-Space Renormalization Group Method Applied to Quantum Lattice Hamiltonians

TL;DR

This paper reviews recent and new results on applying the Real-Space Renormalization Group method to quantum lattice Hamiltonians, focusing on spin systems in one and two dimensions, including non-interacting and interacting cases.

Contribution

It provides a comprehensive review and new insights into the application of the BRG method to quantum spin systems in various dimensions and configurations.

Findings

Analysis of correlations between blocks in non-interacting systems

Application of BRG to interacting 1D and 2D spin systems

Extension to spin ladders and higher-dimensional lattices

Abstract

I review recent work and some new results, performed in collaboration with G. Sierra, on the Real-Space Renormalization group method applied to quantum spin lattice systems mainly in spatial dimensions one and two, and to spin ladders which are somehow in between. The first part of these notes is devoted to non-interacting systems in 1D and 2D and the role played by the correlations between blocks. The second part comprises interacting systems in 1D, spin ladders and 2D using the standard BRG method.