Anderson model

The Anderson Model is a Hamiltonian model that is often used to describe Heavy Fermion systems. The model contains a narrow resonance between a magnetic impurity state and a conduction electron state. The model also contains an on-site repulsion term as found in the Hubbard model between localized electrons. For a single impurity, the Hamiltonian takes the form

where the $f$ operator corresponds to the annihilation operator of an impurity, and $c$ corresponds to a conduction electron annihilation operator, and $sigma$ labels the spin. The onsite Coulomb repulsion is $U$, which is usually the dominant energy scale, and $t\_\{jj\text{'}\}$ is the hopping strength from site $j$ to site $j\text{'}$. A significant feature of this model is the hybridization term $V$, which allows the $f$ electrons in heavy fermion systems to become mobile, despite the fact they are separated by a distance greater than the hill limit.

In heavy-fermion systems, we find we have a lattice of impurities. The relevant model is then the periodic Anderson model.

Bibliography

P.W. Anderson, Phys. Rev. 124 (1961), p. 41