Anderson model
Encyclopedia
The Anderson Impurity Model is a Hamiltonian
model that is often used to describe heavy fermion
systems and Kondo insulators
. 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
operator corresponds to the annihilation operator of an impurity, and 
corresponds to a conduction electron annihilation operator, and 
labels the spin. The onsite 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, 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.
There are other variants of the Anderson model, for instance the SU(4) 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(4) Anderson model Hamiltonian is
where i and i' label the orbital degree of freedom (which can take one of two values), and n represents a number operator.
Hamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
model that is often used to describe heavy fermion
Heavy Fermion
In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons. Electrons, a kind of fermion, found in such materials are sometimes referred to as heavy electrons...
systems and Kondo insulators
Kondo insulator
In solid-state physics, Kondo insulators are understood as materials with strongly correlated electrons, that open up a narrow band gap at low temperatures with the chemical potential lying in the gap, whereas in heavy fermions the chemical potential is located in the...
. The model contains a narrow resonance between a magnetic impurity
Magnetic impurity
A magnetic impurity is an impurity in a host metal that has a magnetic moment. The magnetic impurity can then interact with the conduction electrons of the metal, leading to interesting physics such as the Kondo effect, and heavy fermion behaviour. Some examples of magnetic impurities that metals...
state and a conduction electron state. The model also contains an on-site repulsion term as found in the Hubbard model
Hubbard model
The Hubbard model is an approximate model used, especially in solid state physics, to describe the transition between conducting and insulating systems...
between localized electrons. 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 onsite 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, 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.
There are other variants of the Anderson model, for instance the SU(4) 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
Carbon nanotube quantum dot
A carbon nanotube quantum dot is a small region of a carbon nanotube in which electrons are confined.-Formation:A CNT QD is formed when electrons are confined to a small region within a carbon nanotube...
systems. The SU(4) Anderson model Hamiltonian is
where i and i' label the orbital degree of freedom (which can take one of two values), and n represents a number operator.