Periodic Anderson model vs Anderson impurity model? What is the difference between these two models? I would appreciate if the answer could provide me with some useful references from which I can learn these models.
I saw that periodic Anderson model is solved (in infinite dimensions) using the Anderson impurity model (which is the DMFT as far as I understand), but I would like to understand these models in mode detail.
I would also like to learn how is this connected to DMFT? Are there any good books or pedagogical papers that explain these?
 A: Anderson model
Anderson model describes an impurity coupled to a Fermi sea. This seemingly simple model contains very rich physics - particularly, it exhibits Kondo effect, which had been extensively studied for several decades, and involves many big names and a variety of techniques (a range of diagrammatic approaches, bosonization/orthogonality catastrophe, Bethe ansatz, density functional theory, etc.). As a consequence vast literature is available on the subject. Perhaps the review by Bickers could be a good starting point for further literature search.
Note that another model used for Kondo effect is Kondo model - that of a spin coupled to a Fermi sea. In the regime of interest to Kondo physics, Anderson model can be transformed to Kondo model using Schrieffer-Wolff transformation.
In the last few decades the Anderson model has been extensively used for modeling quantum dots, see, e.g., the series of papers on non-equilibrium transport originating from the publication by Meir, Wingreen and Lee (see also the paper by this group that used the density functional theory)
Periodic anderson model
Periodic Anderson model, as its name correctmy suggests, is a series of Anderson impurities arranged on a lattice. It differs from the Hubbard model in that in the latter the sites are coupled by tunneling, whereas in the periodic Anderson model they are coupled via the Fermi sea (this is a kind of RKKY interaction between magnetic moments). The model is thus interesting for the phase transitions it exhibits, which mix both its Hubbard-like properties (metal-insulator transition), magnetic properties ((anti)ferromagnetic transition), and Kondo physics.
Remark: Anderson model is sometimes called Anderson impurity model to distinguish it from the model used by Anderson in the context of Anderson localization (and perhaps other contributions by this fruitful scientist).
