In order to keep our discussion self-contained, we first briefly review the parafermions and their Fock space. It has been known that, from the $\mathbb{Z}_{p}$ spin degrees of freedom of the clock models, the parafermions are defined by a generalized Jordan-Wigner transformation as[FradkinKadonoff,AlcarazKoberle]{} $$\chi _{2l-1}=\left( \prod_{k<l}\tau _{k}\right) \sigma _{l},\quad \chi
_{2l}=-e^{i\pi /p}\left( \prod_{k\leq l}\tau _{k}\right) \sigma _{l},$$where the $\mathbb{Z}_{p}$ spin operators satisfy the following relations $$\sigma _{l}^{p}=\tau _{l}^{p}=1,\quad \sigma _{l}\tau _{m}=\omega
_{p}^{\delta _{l,m}}\tau _{m}\sigma _{l},$$with $\omega _{p}=e^{i2\pi /p}$. So the algebras of the parafermions are $$\chi _{l}^{p}=1,\quad \chi _{l}^{p-1}=\chi _{l}^{\dagger },\quad \chi
_{l}\chi _{m}=\omega _{p}\chi _{m}\chi _{l},$$for $l<m$. These are the generalized Clifford $\mathbb{Z}_{p}$ graded algebras, and the parafermions are referred to as the Weyl parafermions, because it was first introduced by Weyl[@Weyl1950]. It has been noticed that the second quantized description of the Weyl parafermions is given by the Fock parafermions[@CobaneraOrtiz]. So the basis of $\mathbb{Z}_{p}$ Fock parafermions can be assumed as $|i_{1}i_{2}\cdots i_{L}\rangle $, where $i_{1}$, $i_{2}$, $\cdots $, $i_{L}$ $\in \mathbb{Z}_{p}\equiv \left\{
0,1,2,\cdots ,p-1\right\} $ are the respective occupation numbers of the single particle orbitals. The general structure of the Fock space is defined by $$\mathbb{V}_{F}=\bigoplus_{M=0}^{L(p-1)}\text{Span}\left\{ |i_{1}i_{2}\cdots
i_{L}\rangle ,|\sum_{l=1}^{L}i_{l}=M\right\} .$$In the following the abbreviated notation $|i_{l}\rangle =|0\cdots
