SKYRMION LATTICE MELTING IN THE QUANTUM HALL SYSTEM

The melting and magnetic disordering of the Skyrmion lattice in the qu antum Hall system at filling factor upsilon approximate to 1 are studi ed. A Berezinskii-Kosterlitz-Thouless renormalization-group theory is employed to describe the coupled magnetic and translational degrees of freedom. The nontrivial magnetic properties of the Skyrmion system st em from the in-plane components of the noncollinear magnetization in t he vicinity of Skyrmions, which are described by an antiferromagnetic XY model. In a Coulomb gas formulation the ''particles'' are the topol ogical defects of the XY model (vortices) and of the lattice (dislocat ions and disclinations). The latter frustrate the antiferromagnetic or der and acquire fractional vorticity in order to minimize their energy . We find a number of melting/disordering scenarios for various lattic e types. While these results do not depend on a particular model, we a lso consider a simple classical model for the Skyrmion system. It resu lts in a rich T =0 phase diagram. We propose that the triangular and s quare Skyrmion lattices are generically separated by a centered rectan gular phase in the quantum Hall system, [S0163-1829(98)01740-8].