|
Résumé |
We present the concept of natural super-orbitals for many-body operators, defined as the eigenvectors of the one-body
super-density matrix associated with a vectorized operator. We relate these objects to measures of non-Gaussianity of
operators associated to the occupations of the natural super-orbitals. We first analyze the general analytical properties of
these objects for various typical examples, and then perform a numerical investigation of the natural super-orbitals
corresponding to both the time-evolution operator and a time-evolved local operator in the t-V model and in a quantum
impurity model. Occupations of the natural orbitals for both operators decay exponentially at all times. This indicates that
only a small number of orbitals contribute significantly to quantum correlations, enabling a compact matrix-product-operator
representation. This framework opens the door to future research that leverages the compressed structure of operators in
their natural super-orbital basis, enabling for instance the computation of out-of-time-order correlators in large interacting
systems over extended time scales. |
