Theoretical studies of the two-dimensional interacting electron system in high magnetic field - Brownlie, Matthew (2013)
This is a mathematical study of certain aspects of the interacting electron system in very high perpendicular magnetic field. We analyse restrictions imposed upon the density correlation functions of this system and propose a set of sum rules which they must obey. We study the possibility of building a bosonisation scheme for the projected density operators in the lowest Landau level. We suggest a second order bosonisation, along with an approximation scheme, which may be useful for carrying out calculations in the lowest Landau level. We analyse the possible ground states of the system. We suggest a set of variational wavefunctions which can have lower energy than the Laughlin state for sufficiently soft interaction potentials. We study the collective excitations of the system, paying particular attention to its symmetries. We suggest a set of variational excited states and discuss their applicability to finite as well as infinite systems.