How to generate the NCA input file

In general case, the matrix is a full matrix between the Hilbert subspaces of and electrons. The best choice of base for solving NCA equations is the local eigenbase, where the impurity energies are diagonal. In this case, one needs to write the matrix in local eigenbase as well. First, one can write in direct base, where it is very simple and mostly zero. However, one needs to pay some attention to the fermionic sign that appears due to the fermionic nature of the electron operator . Then, one can transform to the local eigenbase.

The matrix is greatly simplified when the hybridization
is diagonal and Coulomb repulsion is of the form
since in this case, the direct base is also the
local eigenbase. For this case, the program called **generate**
generates the necessary base and calculates the matrix, which is
necessary to run the NCA code.

Let me give a simple example of what the program **generate**
does. In the two band case, with the crystal field splitting,
the local states are

(25) |

where is the total number of electrons on the impurity, is degeneracy of the state and a state represents an atomic state with 2 electrons in the first band and 1 electron in the second. To generate this output, one needs to give the following data to the program

- number of baths : 2
- degeneracy of the first bath : 2
- degeneracy of the second bath: 2

- number of baths : 1
- degeneracy of the bath : N .