# CORE Technology and Exact Hamiltonian Real-Space Renormalization Group Transformations

## TL;DR

The paper introduces the CORE method, a systematic nonperturbative real-space renormalization group approach for Hamiltonian lattice systems, demonstrated on several models and with potential for broader applications.

## Contribution

It presents the CORE technique as a new, systematic way to implement real-space RG transformations nonperturbatively, expanding the toolkit for lattice Hamiltonian analysis.

## Key findings

- Effective in scalar field theory, Heisenberg chain, and Ising chain
- Demonstrates systematic and nonperturbative RG transformations
- Potential applications to Hubbard, t-J models, and lattice gauge theory

## Abstract

The COntractor REnormalization group (CORE) method, a new approach to solving Hamiltonian lattice systems, is presented. The method defines a systematic and nonperturbative means of implementing Kadanoff-Wilson real-space renormalization group transformations using cluster expansion and contraction techniques. We illustrate the approach and demonstrate its effectiveness using scalar field theory, the Heisenberg antiferromagnetic chain, and the anisotropic Ising chain. Future applications to the Hubbard and t-J models and lattice gauge theory are discussed.