A practical scheme for constructing the minimum weight states of the su(n)-Lipkin model in arbitrary fermion number

TL;DR

This paper presents a practical and simplified scheme for constructing minimum weight states in the su(n)-Lipkin model for any fermion number, based on fermion transfer properties and an auxiliary su(2) algebra.

Contribution

It introduces a new, simplified method leveraging fermion transfer properties and an auxiliary su(2) algebra to construct minimum weight states in the su(n)-Lipkin model.

Findings

The scheme is simple and practical.

It applies to arbitrary fermion numbers.

It builds on properties of fermion transfer and auxiliary algebra.

Abstract

With the aim of performing an argument supplement to the previous paper by the present authors, in this paper, a practical scheme for constructing the minimum weight states of the su(n)-Lipkin model in arbitrary fermion number is discussed. The idea comes from the following two points : (i) consideration on the property of one-fermion transfer induced by the su(n)-generators in the Lipkin model and (ii) use of the auxiliary su(2)-algebra presented by the present authors. The form obtained under the points (i) and (ii) is simple.