Conclusion and Perspectives

In this work, correlations in quantum impurity problems have been investigated from the perspective of natural orbitals (NOs), a concept that has been borrowed from the field of quantum chemistry. Quantum impurity problems, within which the Coulomb interaction between electrons occupying the impurity induces strong correlations between particles, exhibit some drastic simplifications when they are expressed through natural orbitals. This representation reveals the hierarchical structure of correlations in these system, in which only a local interaction acts within a large bath of non-interacting particles, compared to fully interacting lattice systems whose correlations are experienced equally by all degrees of freedom.