The Anderson impurity model, named after Philip Warren Anderson, is a Hamiltonian that is used to describe magnetic impurities embedded in metals.
[1] It is often applied to the description of Kondo effect-type problems,[2] such as heavy fermion systems[3] and Kondo insulators[citation needed].
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[1] where the
However, for low enough temperature, the moment is Kondo screened to give non-magnetic many-body singlet state.
[2][3] For heavy-fermion systems, a lattice of impurities is described by the periodic Anderson model.
The hybridization term allows f-orbital electrons in heavy fermion systems to interact, although they are separated by a distance greater than the Hill limit.
There are other variants of the Anderson model, such as the SU(4) Anderson model[citation needed], 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.
label the orbital degree of freedom (which can take one of two values), and