Abstract
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 generalize 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 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 states with ferromagnetic properties.
| Original language | English |
|---|---|
| Pages (from-to) | 195303/1-195303/11 |
| Number of pages | 11 |
| Journal | Physical review. B, Condensed matter and materials physics |
| Volume | 81 |
| Issue number | 19 |
| DOIs | |
| Publication status | Published - 2010 |
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Beugeling, W., Goerbig, M. O. (2010). Chern-Simons theory of multicomponent quantum Hall systems. Physical review. B, Condensed matter and materials physics, 81(19), 195303/1-195303/11. https://doi.org/10.1103/PhysRevB.81.195303
Beugeling, W. ; Goerbig, M.O. ; de Morais Smith, C. / Chern-Simons theory of multicomponent quantum Hall systems. In: Physical review. B, Condensed matter and materials physics. 2010 ; Vol. 81, No. 19. pp. 195303/1-195303/11.
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title = "Chern-Simons theory of multicomponent quantum Hall systems",
abstract = "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 generalize 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 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 states with ferromagnetic properties.",
author = "W. Beugeling and M.O. Goerbig and {de Morais Smith}, C.",
year = "2010",
doi = "10.1103/PhysRevB.81.195303",
language = "English",
volume = "81",
pages = "195303/1--195303/11",
journal = "Physical review. B, Condensed matter and materials physics",
issn = "1098-0121",
publisher = "American Physical Society",
number = "19",
}
Beugeling, W, Goerbig, MO 2010, 'Chern-Simons theory of multicomponent quantum Hall systems', Physical review. B, Condensed matter and materials physics, vol. 81, no. 19, pp. 195303/1-195303/11. https://doi.org/10.1103/PhysRevB.81.195303
Chern-Simons theory of multicomponent quantum Hall systems. / Beugeling, W.; Goerbig, M.O.; de Morais Smith, C.
In: Physical review. B, Condensed matter and materials physics, Vol. 81, No. 19, 2010, p. 195303/1-195303/11.
Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Chern-Simons theory of multicomponent quantum Hall systems
AU - Beugeling, W.
AU - Goerbig, M.O.
AU - de Morais Smith, C.
PY - 2010
Y1 - 2010
N2 - 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 generalize 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 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 states with ferromagnetic properties.
AB - 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 generalize 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 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 states with ferromagnetic properties.
U2 - 10.1103/PhysRevB.81.195303
DO - 10.1103/PhysRevB.81.195303
M3 - Article
SN - 1098-0121
VL - 81
SP - 195303/1-195303/11
JO - Physical review. B, Condensed matter and materials physics
JF - Physical review. B, Condensed matter and materials physics
IS - 19
ER -
Beugeling W, Goerbig MO, de Morais Smith C. Chern-Simons theory of multicomponent quantum Hall systems. Physical review. B, Condensed matter and materials physics. 2010;81(19):195303/1-195303/11. doi: 10.1103/PhysRevB.81.195303
