# A note on the Lipkin model in arbitrary fermion number

## TL;DR

This paper introduces a generalized form of the Lipkin model based on the su(6)-algebra, extending previous work on su(4), and details its algebraic structure and basis parameters.

## Contribution

It presents a new su(6)-algebra-based Lipkin model and provides a complete algebraic framework and basis parameterization for arbitrary fermion numbers.

## Key findings

- Formulation of the su(6)-algebra Lipkin model
- Expression of relations using spherical tensors in su(2)-algebras
- Parameterization of the basis with twenty parameters

## Abstract

A possible form of the Lipkin model obeying the su(6)-algebra is presented. It is a natural generalization from the idea for the su(4)-algebra recently proposed by the present authors. All the relation appearing in the present form can be expressed in terms of the spherical tensors in the su(2)-algebras. For specifying the linearly independent basis completely, twenty parameters are introduced. It is concluded that, in these parameters, the ten denote the quantum numbers coming from the eigenvalues of some hermitian operators. The five in these ten determine the minimum weight state.