fourth_order_tensor¶
- qugradlab.systems.skeletons.fermionic.fermionic_fock_skeleton.fourth_order_tensor(fock_space: FermionSpace) ndarray[int][source]¶
Generates a tensor given by the following expression
where \(c^\dagger_i\) and \(c_i\) are the fermionic creation and anhilation operators acting on the \(i\)th orbital, and \(\alpha\) and \(\beta\) are the rows and columns of the matrix representation of the operator \(c^\dagger_ic_j\) in the Fock basis.\[ u_{i,j,k,l,\alpha,\beta}\coloneqq \left(c^\dagger_ia^\dagger_ja_ka_l\right)_{\alpha,\beta} \]- Parameters:
fock_space (FermionSpace) – The fermionic Fock space
- Returns:
The fourth order skeleton tensor
- Return type:
NDArray[Shape[
fock_space.n_single_particle_states,fock_space.n_single_particle_states,fock_space.n_single_particle_states,fock_space.n_single_particle_states,fock_space.dim,fock_space.dim], int]