Thermodynamic phase diagram of the quantum hall skyrmion system

We numerically study the interacting quantum Hall Skyrmion system based on the Chern-Simons action. By noticing that the action is invariant under global spin rotations in the spin space with respect to the magnetic field direction, we obtain the low-energy effective action for a many-Skyrmion system. Performing extensive molecular dynamics simulations, we establish the thermodynamic phase diagram for a many-Skyrmion system.