Activation energy in a quantum Hall ferromagnet and non-Hartree-Fock skyrmions

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 Land\'e factor) is considered as a smooth nonuniform rotation in three-dimensional spin space. The result within the framework of an excitonically diagonalized part of the Coulomb Hamiltonian can be obtained by any ratio rC=(e²/εlB)/ωc [where e²/εlB is the typical Coulomb energy (lB being the magnetic length); ωc is the cyclotron frequency], and 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 rC (if supposing rC to be small) with use of the total Hamiltonian. When extrapolated to the region rC~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.