Effects of disorder and interactions in the quantum Hall ferromagnet

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 nu=1. 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 noninteracting one. The latter is a nonperturbative 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 the 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.