Fulbright Scholar at Louisiana State University II: Consistent description of quantum criticality of correlated electrons

Abstract: The main objective of my project at LSU was to make diagrammatic approximations thermodynamically consistent near quantum critical points in strongly correlated electron systems. The standard way to achieve thermodynamic consistency is to use the Baym-Kadanoff conserving scheme. This scheme works, however, only unless we meet singularities in correlation functions, which signal quantum critical points.
We analyze the reasons for the breakdown of standard self-consistent approximations of the Baym scheme at the quantum critical point. We discuss the two relevant exact relations between one and two-electron functions and our inability to satisfy them simultaneously. We show that we can restore at least qualitative consistency in that the critical points, singularities in the correlation functions, and emergence of the thermodynamic order due to a symmetry-breaking one-electron self-energy coincide. Only with this consistency we can reliably describe quantum critical behavior. We exemplify the procedure on the Kondo behavior in impurity models.