Activation Energy in a Quantum Hall Ferromagnet and Non-Hartree-Fock Skyrmions

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The energy of Skyrmions is calculated with the help of a technique based on the excitonic representation: the basic set of one-exciton states is used for the perturbation-theory formalism instead of the basic set of one-particle states. We use the approach, at which a skyrmion-type excitation (at zero Lande factor) is considered as a smooth non-uniform rotation in the 3D spin space. The result within the framework of an excitonically diagonalized part of the Coulomb Hamiltonian can be obtained by any ratio r C=(e²/εlB)/ℏ ωc [where e²/εlB is the typical Coulomb energy (lB being the magnetic length); ωc is the cyclotron frequency], and the Landau-level mixing is thereby taken into account. In parallel with this, the result is also found exactly, to second order in terms of the r C (if supposing r C to be small) with use of the total Hamiltonian. When extrapolated to the region r C 1, our calculations show that the skyrmion gap becomes substantially reduced in comparison with the Hartree-Fock calculations. This fact brings the theory essentially closer to the available experimental data.