Unitary Correlation Operator Method and Similarity Renormalization Group: Connections and Differences

TL;DR

This paper compares the Unitary Correlation Operator Method and Similarity Renormalization Group, highlighting their connections, differences, and similar effectiveness in nuclear many-body calculations.

Contribution

It establishes a formal link between SRG and UCOM, proposes a mapping procedure, and compares their effective interactions in nuclear calculations.

Findings

Both methods produce similar convergence in light nuclei.

They exhibit different systematic behaviors with increasing particle number.

The paper provides a formal connection and a practical mapping between the two methods.

Abstract

We discuss relations and differences between two methods for the construction of unitarily transformed effective interactions, the Similarity Renormalization Group (SRG) and Unitary Correlation Operator Method (UCOM). The aim of both methods is to construct a soft phase-shift equivalent effective interaction which is well suited for many-body calculations in limited model spaces. After contrasting the two conceptual frameworks, we establish a formal connection between the initial SRG-generator and the static generators of the UCOM transformation. Furthermore we propose a mapping procedure to extract UCOM correlation functions from the SRG evolution. We compare the effective interactions resulting from the UCOM-transformation and the SRG-evolution on the level of matrix elements, in no-core shell model calculations of light nuclei, and in Hartree-Fock calculations up to 208-Pb. Both interactions exhibit very similar convergence properties in light nuclei but show a different systematic behavior as function of particle number.