triqs.operators.util.U_matrix.transform_U_matrix

triqs.operators.util.U_matrix.transform_U_matrix(U_matrix, T)

Transform a four-index interaction matrix into another basis. The transformation matrix is defined such that new creation operators \(b^\dagger\) are related to the old ones \(a^\dagger\) as

\[b_{i \sigma}^\dagger = \sum_j T_{ij} a^\dagger_{j \sigma}.\]

Parameters:

• U_matrix (float numpy array) – The four-index interaction matrix in the original basis.

• T (real/complex numpy array, optional) – Transformation matrix for basis change. Must be provided if basis=’other’.

Returns:

U_matrix – The four-index interaction matrix in the new basis.

Return type:

float numpy array