The homogeneous electron gas is a widely used model in quantum many-particle physics. It is also known as the fermion one component plasma, Jellium or electron liquid and constitutes a natural testing ground for new methods and approximations due its simple nature and the large volume of analytical and numerical work that has already been performed on it. Moreover, the translational and rotational invariance that is present in the Hamiltonian leads to substantial simplifications in its treatment.
The electron gas is most commonly used as a first approximation of metals where the the valence electrons are weakly bound to the ionic cores. These are the free electron metals, examples of which include the alkali metals. Additionally, the model is fundamental to the practical implementation of density functional theory. In particular, it is the basic ingredient of both the local density and gradient correction approximations.
More relevantly for the present study, the system is found to display a complex phase diagram including a Wigner crystal and a number of exotic magnetic structures. The homogeneous electron gas provides, in fact, the simplest model in which such non-trivial magnetic structures and electron localization can be obtained just by varying one parameter, namely the electronic density.
These facts are responsible for many years of extensive investigation of the static and dynamical properties of the system. A brief historical overview of the major developments is given in the next section. A more comprehensive introduction may be found in the book by Mahan [50].