Excitations in the Interacting Electron Gas

Abstract

However interesting it may be to calculate the total energy of the electron system, which is an essential component of the cohesive energy of solids, as precisely as possible, it is even more important to know the energies of the excited states of electrons if we want to study the physical properties of solids. These calculations are made possible by the quasiparticle picture which is valid for the low-lying excitations. Even if the ground-state wavefunction of the interacting many-body system is not known, adding (removing) a few electrons to (from) the ground state can be interpreted as if a few quasiparticles with renormalized energies \(\widetilde{\varepsilon}_{{\boldsymbol{k}}}\) were added (removed) to (from) the system. Therefore as far as the thermal, electric, or magnetic properties are considered, in which the low-lying excited states play a dominant role, normal metals can be viewed as if independent, free electronlike quasiparticles with renormalized energies were propagating in it. That is the reason why the Drude and Sommerfeld models were so successful in describing the properties of simple metals. In this chapter, these quasiparticles will be studied going beyond the Hartree–Fock approximation.