Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2009-09-21
Phys. Rev. B81:195303,2010
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
11 pages, shortened version, accepted for publication in Phys. Rev. B
Scientific paper
10.1103/PhysRevB.81.195303
The Chern-Simons approach has been widely used to explain fractional quantum Hall states in the framework of trial wave functions. In the present paper, we generalise the concept of Chern-Simons transformations to systems with any number of components (spin or pseudospin degrees of freedom), extending earlier results for systems with one or two components. We treat the density fluctuations by adding auxiliary gauge fields and appropriate constraints. The Hamiltonian is quadratic in these fields and hence can be treated as a harmonic oscillator Hamiltonian, with a ground state that is connected to the Halperin wave functions through the plasma analogy. We investigate several conditions on the coefficients of the Chern-Simons transformation and on the filling factors under which our model is valid. Furthermore, we discuss several singular cases, associated with symmetric states.
Beugeling W.
Goerbig Mark O.
Smith Christopher M.
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