Is it possible to obtain quasiparticle spectrum from standard Hamiltonian spectrum?

2018-03-21 11:17:48

In many papers one can finds quasiparticle energy $\mathcal E_n$ spectrum for BCS like Hamiltonian $\hat H$ (with eigenvalues $E_n$), which is ussualy obtained from diagonalisation of transformed Hamiltonian $\hat H$ into BdG formalism $\hat{\mathcal{H}}_{\text{BdG}}$.

For example figure 7 from:

Is it possible to construct similar spectrum $\mathcal E_n$ using energy spectrum $E_n$ of not transformed Hamiltonian $\hat H$?