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Paper IPM / Physic / 6593  


Abstract:  
We report the application of the nonlinear σ model to study the
multiskyrmion problem in the quantum Hall ferromagnet system. We make use of
a firstprinciple calculation to derive an analytical form for the
interskyrmionic interaction to 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 and a continuous transition into
antiferromagnet square lattice occurs by increasing the skyrmion density and
therefore [ν−1]. Using these results we demonstrate that the transition
for a triangular to a square lattice which was previously derived, using the
HartreeFock method, can also be seen in the field theory picture. We
investigate the possibility that the skyrmions bound in pair 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 superconductorinsulator and the
nonzero temperature phase transitions.
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