This article reviews quantum cluster theories, a set of approximations for infinite lattice
models which treat correlations within the cluster explicitly, and correlations at longer length …

We present explicit expressions for the high-frequency asymptotic behavior of electron self-
energy of general quantum impurity models, which may be useful for improving the …

We derive the first two moment sum rules of the conduction electron retarded self-energy for
both the Falicov–Kimball model and the Hubbard model coupled to an external spatially …

The general problem of representing the Greens function G (k, z) in terms of self-energy in
field theories lacking Wick's theorem is considered. A simple construction shows that a …

Spectral moment sum rules are presented for the inhomogeneous many-body problem
described by the fermionic Falicov-Kimball or Hubbard models. These local sum rules allow …

We report a superconducting transition in the fully conserving fluctuation exchange
approximation for a two-dimensional attractive Hubbard model. The transition temperature …

We explicitly calculate the four leading-order terms of the formal asymptotic series for large|
ε|(where ε denotes the external energy parameter) of the single-particle Green function G σ …

In this thesis we address the problem of electronic correlations in nanoscopic systems. In
general, electronic correlations are of importance for understanding the physics of transition …

The Ward identities for the charge and heat currents are derived for particle-particle and
particle-hole pairs. They are the exact constraints on the current-vertex functions imposed by …

Realistically describing the electronic structure of materials with strongly correlated
electrons, like materials with open d-or f-shells, is one of the great challenges of modern …