The Similarity Renormalization Group for Three-Body Interactions in One Dimension

TL;DR

This paper demonstrates how the similarity renormalization group (SRG) effectively simplifies three-body interactions in a one-dimensional bosonic system, preserving physical results while enabling more efficient calculations.

Contribution

It presents a novel implementation of SRG for three-body interactions in 1D systems, showing how it decouples momentum sectors and maintains observable invariance.

Findings

SRG preserves three-body sector results.

Decouples low- and high-momentum states.

Simplifies numerical calculations of observables.

Abstract

We report on recent progress of the implementation of the similarity renormalization group (SRG) for three-body interactions in a one-dimensional, bosonic model system using the plane wave basis. We discuss our implementation of the flow equations and show results that confirm that results in the three-body sector remain unchanged by the transformation of the Hamiltonian. We also show how the SRG transformation decouples low- from high-momentum nodes in the three-body sector and therefore simplifies the numerical calculation of observables.