A possible framework of the Lipkin model obeying the su(n)-algebra in arbitrary fermion number. I --- The su(2)-algebras extended from the conventional fermion-pair and determination of the minimum weight states ---

TL;DR

This paper systematically investigates the minimum weight states of the Lipkin model with n levels obeying su(n)-algebra, extending the su(2)-algebra approach to arbitrary fermion numbers and levels.

Contribution

It introduces a framework using su(2)-algebras independent of su(n)-algebra to determine minimum weight states for any fermion number in the Lipkin model.

Findings

Minimum weight states are explicitly determined for n=2, 3, 4, 5.

The framework includes the conventional minimum weight state with all fermions in the lowest level.

The approach generalizes the su(2)-algebra method to su(n)-algebra for arbitrary levels.

Abstract

The minimum weight states of the Lipkin model consisting of n single-particle levels and obeying the su(n)-algebra are investigated systematically. The basic idea is to use the su(2)-algebra which is independent of the su(n)-algebra. This idea has been already presented by the present authors in the case of the conventional Lipkin model consisting of two single-particle levels and obeying the su(2)-algebra. If following this idea, the minimum weight states are determined for any fermion number occupying appropriately n single-particle levels. Naturally, the conventional minimum weight state is included: all fermions occupy energetically the lowest single-particle level in the absence of interaction. The cases n=2, 3, 4 and 5 are discussed in rather detail.