Effects of Disorder and Interactions in the Quantum Hall Ferromagnet

TL;DR

This paper investigates how disorder and electron interactions influence the quantum Hall ferromagnet, revealing a disorder-driven quantum phase transition from a ferromagnetic state to a spin glass phase using a bosonic reformulation of the model.

Contribution

It introduces a non-perturbative bosonic approach to study disorder effects in quantum Hall ferromagnets, accounting for interactions up to the RPA level.

Findings

Disorder can induce a quantum phase transition in the system.

The transition is from a ferromagnetic to a spin glass phase.

The approach allows for a fully quantum treatment including interactions.

Abstract

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.