Noncommutative field theory description of quantum Hall skyrmions

Abstract

We revisit the quantum Hall system with no Zeeman splitting energy using the noncommutative field theory. We analyze the BPS condition for the delta-function interaction near the filling factor $\nu =1$. Multi-skyrmions are shown to saturate the BPS bounds. The dimension of the moduli space of $k$ skyrmions is $4k+2$. Advantage of the noncommutative field description is demonstrated through the derivation of the effective nonlinear $\sigma$ model Lagrangian.

23 pages, Revtex, more references added in

References in corpus (6)

• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• D-brane Dynamics and the Quantum Hall Effect
• Solitons in 2+1 Dimensional Non-Commutative Maxwell Chern-Simons Higgs Theories
• Nielsen-Olesen vortices in noncommutative space
• Self-dual Chern-Simons solitons in noncommutative space
• Noncommutative Solitons

Cited by in corpus (10)

• Orbital Magnetism of Two-Dimension Noncommutative Confined System
• Unitarity in space-time noncommutative field theories
• Non-relativistic electron-electron interaction in a Maxwell-Chern-Simons-Proca model endowed with a timelike Lorentz-violating background
• Topological Solitons in Noncommutative Plane and Quantum Hall Skyrmions
• Bulk and edge excitations of a $\nu =1$ Hall ferromagnet
• Microscopic Theory of Skyrmions in Quantum Hall Ferromagnets
• Solitons of Sigma Model on Noncommutative Space as Solitons of Electron System
• Induced commutative Chern-Simons term from noncommutativity in planar systems
• Non-commutative field theory approach to two-dimensional vortex liquid system
• Planar field theories with space-dependent noncommutativity