Bosonization approach for quantum Hall ferromagnets

Ricardo Doretto

Utrecht University



Subject: non-perturbative bosonization approach for quantum Hall systems; spin excitations; bilayer quantum Hall systems. description: In the last few years, I have been working with a non-perturbative bosonization method for the quantum Hall system at filling factor one [1], which I developed during my PhD. Within this formalism, We show that the elementary neutral (spin) excitations of the quantum Hall system at filling factor one, known as magnetic excitons, can be treated approximately as bosons. By applying the method to the interacting system, we show that the fermionic Hamiltonian is mapped into an interacting bosonic model [1].
The dispersion relation of the bosons recovers previous diagrammatic calculations of Kallin and Halperin. Moreover, the boson interaction term accounts for the formation of bound states of two-bosons. We show that there is a relation between these excitations and the skyrmion-antiskyrmion pair ones, in analogy with the ferromagnetic Heisenberg model.
The formalism was also applied to calculate spin excitations of the fractional quantum Hall system at filling factors 1/3 and 1/5 [2], within the framework of the Hamiltonian theory of Shankar and Murthy for the fractional quantum Hall effect.
Finally, the bilayer quantum Hall system at total filling factor one has been studied within this formalism. Here, we are able to calculate the dispersion relation of the quasiparticles and also show that a Bose-Einstein condensate of interlayer excitons is instable as the distance between the two layers increases [3].

[1] Lowest Landau level bosonization R. L. Doretto, A. O. Caldeira, and S. M. Girvin, Phys. Rev. B 71, 045339 (2005)
[2] Spin-excitations of the quantum Hall ferromagnet of composite fermions R. L. Doretto, M. O. Goerbig, P. Lederer, A. O. Caldeira, and C. Morais Smith, Phys. Rev. B 72, 035341 (2005)
[3] A bosonization approach for bilayer quantum Hall systems at \nu_T=1 R. L. Doretto, A. O. Caldeira, and C. Morais Smith, cond-mat/0511315