We investigate the ground state of the 2D electron gas in the quantum Hall regime at a filling factory slightly deviating from unity, which can be viewed as a sparse lattice of Skyrmions. We have found that in the low density limit Skyrmions are bound in pairs, the latter forming an actual lattice. We have shown that with an increase in density the lattice undergoes a quantum phase transition, which is analogous to the superconducting phase transition in Josephson junction arrays.
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Nazarov et al. (1998) studied this question.