  This work treats the effects of disorder and interactions in a quantum Hall
ferromagnet, which is realized in a two-dimensional electron gas (2DEG) in a
perpendicular magnetic field at Landau level filling factor equal one. We study
the problem by projecting the original fermionic Hamiltonian into magnon
states, which behave as bosons in the vicinity of the ferromagnetic ground
state. The approach permits the reformulation of a strongly interacting model
into a non-interacting one. The latter is a non-perturbative scheme that
consists in treating the two-particle neutral excitations of the electron
system as a bosonic single-particle. Indeed, the employment of bosonization
facilitates the inclusion of disorder in the study of the system. It has been
shown previously that disorder may drive a quantum phase transition in the Hall
ferromagnet. However, such studies have been either carried out in the
framework of nonlinear sigma model, as an effective low-energy theory, or
included the long-range Coulomb interaction in a quantum description only up to
the Hartree-Fock level. Here, we establish the occurrence of a disorder-driven
quantum phase transition from a ferromagnetic 2DEG to a spin glass phase by
taking into account interactions between electrons up to the random phase
approximation level in a fully quantum description.
