JMP  Vol.6 No.12 , September 2015
Alternative Derivation of the Mean-Field Equations for Composite Fermions
ABSTRACT
The Hamiltonian describing a composite fermion system is usually presented in a phenomenological way. By using a classical nonrelativistic U(1) × U(1) gauge field model for the electromagnetic interaction of electrons, we show how to obtain the mean-field Hamiltonian describing composite fermions in 2 + 1 dimensions. In order to achieve this goal, the Dirac Hamiltonian formalism for constrained systems is used. Furthermore, we compare these results with the ones corresponding to the inclusion of a topological mass term for the electromagnetic field in the Lagrangian.

Cite this paper
Manavella, E. and Repetto, C. (2015) Alternative Derivation of the Mean-Field Equations for Composite Fermions. Journal of Modern Physics, 6, 1737-1742. doi: 10.4236/jmp.2015.612175.
References
[1]   Jain, J.K. and Anderson, P.W. (2009) Proceedings of the National Academy of Sciences of the United States of America,
106, 9131-9134.
http://dx.doi.org/10.1073/pnas.0902901106

[2]   Lu, H., Das Sarma, S. and Park, K. (2010) Physical Review B, 82, 201303(R).
http://dx.doi.org/10.1103/PhysRevB.82.201303

[3]   Girvin, S.M. and MacDonald, A.H. (1987) Physical Review Letters, 58, 1252-1255.
http://dx.doi.org/10.1103/PhysRevLett.58.1252

[4]   Zhang, S.C., Hansson, T.H. and Kivelson, S.A. (1989) Physical Review Letters, 62, 82-85.
http://dx.doi.org/10.1103/PhysRevLett.62.82

[5]   Jain, J.K. (1989) Physical Review Letters, 63, 199-202.
http://dx.doi.org/10.1103/PhysRevLett.63.199

[6]   Schrieffer, J.R. (1964) Theory of Superconductivity. W.A. Benjamin, Inc., New York.

[7]   Mahan, G.D. (2000) Many-Particle Physics. 3rd Edition, Kluwer Academic/Plenum Publishers, New York.
http://dx.doi.org/10.1007/978-1-4757-5714-9

[8]   Manavella, E.C. (2001) International Journal of Theoretical Physics, 40, 1453-1474.
http://dx.doi.org/10.1023/A:1017505511427

[9]   Manavella, E.C. and Addad, R.R. (2009) International Journal of Theoretical Physics, 48, 2473-2485.
http://dx.doi.org/10.1007/s10773-008-9925-5

[10]   Halperin, B.I., Lee, P.A. and Read, N. (1993) Physical Review B, 47, 7312-7343.
http://dx.doi.org/10.1103/PhysRevB.47.7312

[11]   Lopez, A. and Fradkin, E. (2003) Fermionic Chern-Simons Field Theory for the Fractional Hall Effect. In: Heinonen, O., Ed., Composite Fermions, World Scientific, Singapore.

[12]   Lopez, A. and Fradkin, E. (1991) Physical Review B, 44, 5246-5262.
http://dx.doi.org/10.1103/PhysRevB.44.5246

[13]   Jain, J.K. (2007) Composite Fermions. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511607561

[14]   Greiner, W. and Reinhardt, J. (1996) Field Quantization. Springer-Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-642-61485-9

[15]   Jackiw, R. and Templeton, S. (1981) Physical Review D, 23, 2291-2304.
http://dx.doi.org/10.1103/PhysRevD.23.2291

 
 
Top