Conservation in strongly correlated systems - A practical viewpoint

Abstract: Theorists are in search of an improved dynamical mean-field theory (DMFT) for strongly correlated systems, but so far no proposed method can match its elegance. One aspect of the latter is the satisfaction of conservation laws and of the associated Ward identities. This leads to thermodynamic consistency and to a sound description of collective modes. Recently developed methods allow a feedback of these modes on the local physics by modifying the interaction of the auxiliary impurity model of DMFT. Are these attempts at odds with its conserving character? The answer to this question improves our understanding of auxiliary impurity models, as well as the role of self-consistency conditions.