Proper derivation of subspace mapping from whole space mapping in boson expansion theory

TL;DR

This paper demonstrates that the norm operator method enables proper derivation of subspace mapping from whole space mapping in boson expansion theory, correcting previous misconceptions and clarifying the role of phonon contributions.

Contribution

It introduces the norm operator method to accurately derive subspace mapping, addressing limitations of conventional BETs and clarifying the applicability of the boson expansion theory.

Findings

Proper derivation of subspace mapping using the norm operator method.

Correction of misconceptions in conventional BET claims.

Demonstration of the Park operator's effectiveness in subspace mapping.

Abstract

The norm operator method, which was recently proposed as a new formulation of the boson expansion theory (BET), is used to show that the subspace mapping is properly derived from the whole space mapping. This derivation requires the appropriate renormalization of the contribution of phonons that are not adopted as boson excitations in the subspace mapping. This was impossible with conventional BETs (which ignore these contributions), and is only made possible for the first time by the norm operator method, which treats these contributions appropriately. We also correct the confusion in the claims of conventional BETs. Namely, contrary to conventional claims, we show that when the phonon excitations not adopted as boson excitations make no contribution at all, the subspace mapping is obtained simply by discarding those excitations. Furthermore, we demonstrate that the Park operator, which had been considered effective only in the whole space mapping, is also effective in the subspace mapping. These findings provide a clear criterion for verifying the applicability of the boson expansion theory to large-amplitude collective motions and offer a new perspective on a microscopic foundation of the interacting boson model (IBM).