On the high-temperature expansion for a partially filled lowest Landau level

We study the two-dimensional interacting electron gas in a strong magnetic field in the limit in which all electrons are confined to the lowest Landau level. Reconsidering the high-temperature expansion of the grand canonical thermodynamic potential performed in the work by Zheng and MacDonald, we push the exact expansion up to the seventh order in the interaction. This is done with a method known from expansions in spin systems. The equivalence of this method with the many-body perturbation treatment is explicitly checked up to the third order. We evaluate the series for the case of the short-range electron–electron interaction. As an application, we study the temperature-dependent energy. It shows indications of a cusp developing, as expected, at the filling factor View the MathML source as temperature is lowered. We confirm this result by extrapolating the energy to zero temperature.