Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives

TL;DR

This paper investigates the convergence properties of Contractor Renormalization (CORE) in 2D Heisenberg Antiferromagnets and offers new perspectives to enhance its accessibility and applicability, especially in quantum information science.

Contribution

It provides a detailed analysis of cluster expansion convergence in CORE and proposes a new scheme for defining terms, along with insights to broaden its use in quantum information.

Findings

Different blocking schemes reveal unexpected results.

A new scheme for defining cluster expansion terms is suggested.

Discussion on improving and generalizing CORE methods.

Abstract

Contractor Renormalization (CORE) is a numerical renormalization method for Hamiltonian systems that has found applications in particle and condensed matter physics. There have been few studies, however, on further understanding of what exactly it does and its convergence properties. The current work has two main objectives. First, we wish to investigate the convergence of the cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This is important because the linked cluster expansion used to evaluate this formula non-perturbatively is not controlled by a small parameter. Here we present a study of three different blocking schemes which reveals some surprises and in particular, leads us to suggest a scheme for defining successive terms in the cluster expansion. Our second goal is to present some new perspectives on CORE in light of recent developments to make it accessible to more researchers, including those in Quantum Information Science. We make some comparison to entanglement-based approaches and discuss how it may be possible to improve or generalize the method.