2 M ay 1 99 7 The field theory of Skyrme lattices in quantum Hall ferromagnets

We report the application of the nonlinear σ model to study the multiskyrmion problem in the quantum Hall ferromagnet system. We show that the ground state of the system can be described by a ferromagnet triangular Skyrme lattice near ν = 1 where skyrmions are extremely dilute. We find a transition into antiferromagnet square lattice by increasing the skyrmion density and therefore |ν−1|. We investigate the possibility that the square Skyrme lattice deforms to a single skyrmion with the same topological charge when the Zeeman energy is extremely smaller than the Coulomb energy. We explicitly show that the energy of a skyrmion with charge two is less than the energy of two skyrmions each with charge one when g ≤ gc. By taking the quantum fluctuations into account, we also argue the possibility of the existence of a non-zero temperature Kosterlitz-Thouless and a superconductor-insulator phase transition. Typeset using REVTEX 1