# Interacting resonant level model

1. Oct 25, 2014

### gonadas91

Hey guys this
is my first question, I am trying to solve a first approach of the interacting resonant level model (IRLM), where we suppose that there is only one energy level acting as a quantum dot between the leads. The hamiltonian is of the form

\begin{eqnarray}
H=\sum_{kL}\epsilon_{kL} c_{kL}^{\dagger}c_{kL} + \sum_{kR}\epsilon_{kR} c_{kR}^{\dagger}c_{kR} - t \sum_{kL,kR}\phi_{kL(0)}\phi_{kR(0)}^* c_{kL}^{\dagger}c_{kR} + \phi_{kL(0)}^* \phi_{kR(0)} c_{kR}^{\dagger}c_{kL}
\end{eqnarray}

where the $c_{ks}^{\dagger} , c_{ks}$ with $s=L,R$ refers to the fermionic creation/annihilation operators n the left and right lead respectively. The $\phi_{ks} (0)$ are the eigenfunctions of the single particle hamiltonian when we have a delta function as a barrier ($\delta (x)$)at $x=0$, that is the single particle equivalent problem.\\

I would like to express the hamiltonian in another basis, where it is diagonalised and that also had fermionic operators, but I have just tried a Bogoliubov transformation for fermions and realized that I cant, because the u and v parameters become sines and cosines and in some time I get a divergence with the anticommutation relations. Does anyone know how to solve this? Thank you!!

2. Oct 30, 2014

### Staff: Admin

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

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