Abstract
Within the Grassmannian U(2N)/U(N) × U(N) nonlinear σ-model representation of localization, one can study the low-energy dynamics of both a free and interacting electron gas. We study the crossover between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping.
Similar content being viewed by others
References
A. M. M. Pruisken and M. A. Baranov, Europhys. Lett. 31, 543 (1995), and references therein.
A. M. M. Pruisken, M. A. Baranov, and B. Škorić, Phys. Rev. B 60, 16 807 (1999).
M. A. Baranov, A. M. M. Pruisken, and B. Škorić, Phys. Rev. B 60, 16 821 (1999).
A. M. M. Pruisken, B. Škorić, and M. A. Baranov, Phys. Rev. B 60, 16 838 (1999).
B. Škorić and A. M. M. Pruisken, Nucl. Phys. B 559, 637 (1999).
M. A. Baranov, I. S. Burmistrov, and A. M. M. Pruisken, Phys. Rev. B 66, 075317 (2002).
A. M. M. Pruisken, Phys. Rev. Lett. 61, 1297 (1988).
A. M. Finkelstein, Pis’ma Zh. Éksp. Teor. Fiz. 37, 436 (1983) [JETP Lett. 37, 517 (1983)]; Zh. Éksp. Teor. Fiz. 86, 367 (1984) [Sov. Phys. JETP 59, 212 (1984)]; Physica B (Amsterdam) 197, 636 (1994).
C. Castellani, C. Di Castro, P. A. Lee, and M. Ma, Phys. Rev. B 30, 527 (1984).
For a recent review see A. M. M. Pruisken and I. S. Burmistrov}, Ann. Phys. (N.Y.)} 316}, 285 (200
See, e.g., Composite Fermions}, Ed. by O. Heinonen} (World Sci., Singapore}, 199
J. K. Jain, Phys. Rev. Lett. 63, 199 (1989).
A. M. M. Pruisken, M. A. Baranov, and M. Voropaev, cond-mat/0206011 (unpublished).
See, e.g., D. G. Polyakov and B. I. Shklovskii}, Phys. Rev. Lett.} 73}, 1150 (1994}). Their idea of “one parameter scaling,” however, is in conflict with our resu
D. Pines and P. Noziéres, Theory of Quantum Liquids (Benjamin, New York, 1966; Mir, Moscow, 1967).
E. Brezin, S. Hikami, and J. Zinn-Justin, Nucl. Phys. B 165, 528 (1980).
A. M. M. Pruisken, Phys. Rev. B 31, 416 (1985).
I. S. Burmistrov, M. A. Baranov, and A. M. M. Pruisken (unpublished).
H. P. Wei, D. C. Tsui, M. A. Palaanen, and A. M. M. Pruisken, Phys. Rev. Lett. 61, 1294 (1988).
R. T. F. van Schaijk, A. de Visser, S. M. Olsthoorn, et al., Phys. Rev. Lett. 84, 1567 (2000).
D. T. N. de Lang, L. A. Ponomarenko, A. de Visser, et al., Physica E (Amsterdam) 12, 666 (2002).
A. M. M. Pruisken, D. T. N. de Lang, L. A. Ponomarenko, and A. de Visser, cond-mat/0109043 (unpublished).
A. M. M. Pruisken, M. A. Baranov, and M. Voropaev, cond-mat/0101003 (unpublished).
A. M. M. Pruisken and I. S. Burmistrov, cond-mat/0502488 (unpublished).
Author information
Authors and Affiliations
Additional information
From Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 82, No. 3, 2005, pp. 166–170.
Original English Text Copyright © 2005 by Pruisken, Baranov, Burmistrov.
The text was submitted by the authors in English.