Field theory of Skyrme lattices in quantum Hall ferromagnets

We report the application of the nonlinear sigma model to study the multiskyrmion problem in the quantum Hall ferromagnet system. We make use of a first-principles calculation Co derive an analytical form for the interskyrmionic interaction to show that the ground state of the system can be described by a ferromagnetic triangular Skyrme lattice near upsilon=1 where skyrmions are extremely dilute and a continuous transition into an antiferromagnetic square lattice occurs by increasing the skyrmion density and therefore \upsilon-1\. Using these results we demonstrate that the transition for a triangular to a square lattice which was previously derived, using the Hartree-Fock method, can also be seen in the field theory picture. We investigate the possibility that the skyrmions bind in pairs to make a biskyrmion triangular lattice when the Zeeman energy is extremely small. We show that the energy of a skyrmion with charge Q is less than the energy of Q skyrmions each with charge one when the short-range interaction among them is considered. By taking the quantum fluctuations into account, we also argue the possibility of the existence of a superconductor-insulator and the nonzero-temperature phase transitions. [S0163-1829(98)05839-1].