Bootstrap Approximations in Contractor Renormalization

TL;DR

This paper introduces a bootstrap approach to improve the Contractor Renormalization method for analyzing quantum spin models, revealing phase behaviors but highlighting scheme dependencies.

Contribution

The paper presents a bootstrap technique for the CORE method, enabling better approximation of long-range interactions in quantum spin systems.

Findings

Successfully identified the Neel phase in the 2D Heisenberg antiferromagnet.

Detected a phase transition in the J2-J1 model with weak frustration.

Highlighted dependencies on blocking and truncation schemes affecting results.

Abstract

We propose a bootstrap method for approximating the long-range terms in the Contractor Renormalization (CORE) method. The idea is tested on the 2-D Heisenberg antiferromagnet and the frustrated J_2-J_1 model. We obtain renormalization group flows that directly reveal the Neel phase of the unfrustrated HAF and the existence of a phase transition in the J_2-J_1 model for weak frustration. However, we find that this bootstrap method is dependent on blocking and truncation schemes. For this reason, we discuss these dependencies and unresolved issues that researchers who use this approach must consider.