DOI: 10.1063/1.531921. Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker

Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker–Coddington model

10.1063/1.531921

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

Abstract

An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N=1 is known to describe the critical behavior at the plateau transition in systems exhibiting the integer quantum Hall effect. Using a recently discovered equality of integrals, the network model is transformed into a lattice field theory defined over Efetov’s σ model space with unitary symmetry. The transformation is exact for all N, no saddle-point approximation is made, and no massive modes have to be eliminated. The naive continuum limit of the lattice theory is shown to be a supersymmetric version of Pruisken’s nonlinear σ model with couplings σxx=N/4 and σxy=N/2 at the symmetric point. It follows that the model for N=2, which describes a spin degenerate Landau level and the random flux problem, is noncritical. On the basis of symmetry considerations and inspection of the Hamiltonian limit, a modified network model is formulated, which still lies in the quantum Hall universality class. The prospects for deformation to a Yang–Baxter integrable vertex model are briefly discussed.

Bibliography

Zirnbauer, M. R. (1997). Toward a theory of the integer quantum Hall transition: Continuum limit of the ChalkerâCoddington model. Journal of Mathematical Physics, 38(4), 2007â2036.

Authors 1

Martin R. Zirnbauer (first)

References 29 Referenced 61

{'key': '2024020622322740000_r1'}
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10.1088/0022-3719/21/14/008 / J. Phys. C / Percolation, quantum tunneling, and the integer quantum Hall effect (1988)
10.1103/PhysRevB.50.10788 / Phys. Rev. B / Network models of quantum percolation and their field-theory representation (1994)
{'key': '2024020622322740000_r5'}
10.1007/BF01319839 / Z. Phys. B / The mobility edge problem: Continuous symmetry and a conjecture (1979)
10.1080/00018738300101531 / Adv. Phys. / Supersymmetry and theory of disordered metals (1983)
10.1016/0550-3213(84)90101-9 / Nucl. Phys. B / On localization in the theory of the quantized Hall effect: A two-dimensional realization of the θ-vacuum (1984)
10.1016/0550-3213(87)90178-7 / Nucl. Phys. B / Quasi particles in the theory of the integral quantum Hall effect (II). Renormalization of the Hall conductance or instanton angle theta (1987)
10.1016/0550-3213(84)90277-3 / Nucl. Phys. B / Theory of the quantized Hall effect (I) (1984)
10.1016/0550-3213(87)90179-9 / Nucl. Phys. B / Single electron in a random potential and a strong magnetic field (1987)
{'key': '2024020622322740000_r12', 'first-page': '552', 'article-title': 'Quantization of Hall conductivity', 'volume': '38', 'year': '1983', 'journal-title': 'JETP Lett.'} / JETP Lett. / Quantization of Hall conductivity (1983)
{'key': '2024020622322740000_r13', 'first-page': '513', 'article-title': 'Towards a theory of the integer quantum Hall transition: From the nonlinear sigma model to superspin chains', 'volume': '3', 'year': '1994', 'journal-title': 'Ann. Phys. (Leipzig)'} / Ann. Phys. (Leipzig) / Towards a theory of the integer quantum Hall transition: From the nonlinear sigma model to superspin chains (1994)
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{'key': '2024020622322740000_r14'}
10.1088/0305-4470/29/22/013 / J. Phys. A / Supersymmetry for systems with unitary disorder: Circular ensembles (1996)
{'key': '2024020622322740000_r16'}
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Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 9:50 a.m.)
Deposited	1 year, 6 months ago (Feb. 6, 2024, 8:19 p.m.)
Indexed	3 weeks, 4 days ago (Aug. 1, 2025, 11:59 p.m.)
Issued	28 years, 4 months ago (April 1, 1997)
Published	28 years, 4 months ago (April 1, 1997)
Published Print	28 years, 4 months ago (April 1, 1997)

Funders 0

None

BibTeX

@article{Zirnbauer_1997, title={Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker–Coddington model}, volume={38}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.531921}, DOI={10.1063/1.531921}, number={4}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Zirnbauer, Martin R.}, year={1997}, month=apr, pages={2007–2036} }

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