A Modified Chern-Simons Term: Chiral Spin Systems and Anyon Superconductivity

Abstract

In this paper, starting from a system of noninteracting spins in a plane and introducing an appropriate density function for spins, we arrive at a metric independent continuum chiral model. The Lagrangian of this model is a variant of the CP 1 Chern-Simons term and is characterized by an interesting variety of gauge and symmetry groups and topological features. Certain significant aspects of this model or variants thereof are also shared by the mean field approach to the anyon gas, the CP 1 model with the Chern-Simons term and the RVB description of the strongly coupled Hubbard model. The class of models studied here may therefore be useful in the investigation of the latter systems.

Properties of Quantum Hall Skyrmions From Anomalies

“…Concerning i), as before, the bulk action is not invariant under gauge transformations (7) of the electromagnetic potentials A µ . In addition, unlike before, it is not invariant under gauge transformations ( 8) of the fields g. From S W Z we pick up the surface term…”

“…A description dual to the Landau-Ginzburg model was found useful for the analysis of vortex dynamics [5]. It is of interest to write down a dual description suitable for the analysis of Skyrmion dynamics as well [6], [7]. This is one of the purposes of our letter.…”

“…where both Λ and λ are functions of space-time coordinates. On the other hand, taking into account the boundary ∂Σ, one finds instead that (7) gives the surface terms…”

“…while gauge invariance under transformations ( 8) persists. We now specify that under gauge transformations (7), the edge field φ transforms according to…”