Linear response of a magnetized electron gas: application to the thermodynamics of aluminium

We first consider the three independent functions that describe the linear response to external perturbations of a non-interacting strongly magnetized electron gas. These functions are needed to build the interacting response to an external perturbation, even if it is purely scalar. The interacting response function is obtained in the local density approximation for the exchange and correlation energy functional . It is singular when the non-interacting Fermi level coincides with a Landau band edge. In addition, the numerical study of the effective local-field factor shows that the response function can also have poles in a region of densities and magnetic fields approximately defined by: and , where is the reference magnetic field . Outside this region, we use the linear response theory applied to a model electron - ion interaction for an estimate of the equation of state of solid aluminium in the presence of strong magnetic fields up to . The densities are in the range 0.8 - 1.5 times the normal density. The results show the importance of the changes induced by the magnetic field, in particular those associated with the localization of the charge density.