Towards a theory of the integer quantum Hall transition: From the nonlinear sigma model to superspin chains
作者:
Martin R. Zirnbauer,
期刊:
Annalen der Physik
(WILEY Available online 1994)
卷期:
Volume 506,
issue 7‐8
页码: 513-577
ISSN:0003-3804
年代: 1994
DOI:10.1002/andp.19945060702
出版商: WILEY‐VCH Verlag
关键词: Integer quantum Hall effect;Metal‐insulator transition;Nonlinear σ model;Supersymmetry;Spin chains
数据来源: WILEY
摘要:
AbstractA careful study of the supersymmetric version of Pruisken's nonlinear σ model for the integer quantum Hall effect is presented. The lattice regularized model is cast in Hamiltonian form by taking the anisotropic limit and interpreting the topological density as an alternating sum of Wess Zumino terms. It is argued that the relevant large‐scale physics of the model is preserved by projection of the quantum Hamiltonian on its sector of degenerate strong‐coupling ground states. For values of the Hall conductivity close toe2/2h(mode2/h), where a delocalization transition occurs, this yields the Hamiltonian of a quantum superspin chain which is closely related to an anisotropic version of the Chalker‐Coddington model. The relation implies that the ratio of magnetic length over potential correlation length is an irrelevant parameter at the transition. The superspin chain resembles a 1disotropic antiferromagnet with spin 1/2. It has an alternating structure which however permits an invariance under translation by one site. The conductance coefficients of a quantum Hall system withNsmall contacts translate intoN‐superspin correlation functions which are governed by conformal invariance. The superspin formalism provides a framework for studying the crossover from classical to quantum percolation. It does not however encompass the frequency‐dependent correlations of wave amplitudes at c
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