Anderson impurity model


The Anderson impurity model, named after Philip Warren Anderson, is a Hamiltonian that is used to describe magnetic impurities embedded in metals. It is often applied to the description of Kondo effect-type problems, such as heavy fermion systems and Kondo insulators. In its simplest form, the model contains a term describing the kinetic energy of the conduction electrons, a two-level term with an on-site Coulomb repulsion that models the impurity energy levels, and a hybridization term that couples conduction and impurity orbitals. For a single impurity, the Hamiltonian takes the form
where the operator corresponds to the annihilation operator of an impurity, and corresponds to a conduction electron annihilation operator, and labels the spin. The on–site Coulomb repulsion is, which is usually the dominant energy scale, and is the hopping strength from site to site. A significant feature of this model is the hybridization term, which allows the electrons in heavy fermion systems to become mobile, although they are separated by a distance greater than the Hill limit.
For heavy-fermion systems, a lattice of impurities is described by the periodic Anderson model:
There are other variants of the Anderson model, for instance the SU Anderson model, which is used to describe impurities which have an orbital, as well as a spin, degree of freedom. This is relevant in carbon nanotube quantum dot systems. The SU Anderson model Hamiltonian is
where and ' label the orbital degree of freedom, and ' represents a number operator.