Anderson impurity model
Hamiltonian used in quantum physics / From Wikipedia, the free encyclopedia
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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 operator is the annihilation operator of a conduction electron, and is the annihilation operator for the impurity, is the conduction electron wavevector, and labels the spin. The on–site Coulomb repulsion is , and gives the hybridization.