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Title: Localization length index and subleading corrections in a Chalker-Coddington model: A numerical study

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Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 91; Journal Issue: 11; Journal ID: ISSN 1098-0121
American Physical Society
Country of Publication:
United States

Citation Formats

Nuding, W., Klümper, A., and Sedrakyan, A. Localization length index and subleading corrections in a Chalker-Coddington model: A numerical study. United States: N. p., 2015. Web. doi:10.1103/PhysRevB.91.115107.
Nuding, W., Klümper, A., & Sedrakyan, A. Localization length index and subleading corrections in a Chalker-Coddington model: A numerical study. United States. doi:10.1103/PhysRevB.91.115107.
Nuding, W., Klümper, A., and Sedrakyan, A. 2015. "Localization length index and subleading corrections in a Chalker-Coddington model: A numerical study". United States. doi:10.1103/PhysRevB.91.115107.
title = {Localization length index and subleading corrections in a Chalker-Coddington model: A numerical study},
author = {Nuding, W. and Klümper, A. and Sedrakyan, A.},
abstractNote = {},
doi = {10.1103/PhysRevB.91.115107},
journal = {Physical Review B},
number = 11,
volume = 91,
place = {United States},
year = 2015,
month = 3

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevB.91.115107

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Cited by: 3works
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  • 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{close_quote}s {sigma} 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{close_quote}s nonlinearmore » {sigma} model with couplings {sigma}{sub xx}=N/4 and {sigma}{sub xy}=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{endash}Baxter integrable vertex model are briefly discussed. {copyright} {ital 1997 American Institute of Physics.}« less
  • We consider the Chalker-Coddington network model for the integer quantum Hall effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models with two loop flavors. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra and parameterized by the loop fugacity n. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-gas theory, whereas the other two branches (3,4) couplemore » the two loop flavors, and relate to an SU(2){sub r}xSU(2){sub r}/SU(2){sub 2r} Wess-Zumino-Witten (WZW) coset model for the particular values n=-2cos[{pi}/(r+2)], where r is a positive integer. The truncated Chalker-Coddington model is the n=0 point of branch 4. By numerical diagonalization, we find that its universality class is neither an analytic continuation of the WZW coset nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.« less
  • We study the Nambu-Goto model numerically for a string of finite length at an arbitrary temperature. The static quark-antiquark potential is investigated and it is found that the deconfinement radius [ital r][sub dec] (the distance between quarks for which the potential vanishes) is independent of the temperature. For [tau]=[tau][sub dec] (the temperature for which the string tension vanishes), the potential becomes a constant for large [ital r], thus losing its confining'' property. This is clearly a consistent result with the interpretation of [tau][sub dec] as a deconfinement temperature. For [tau][gt][tau][sub dec], solutions to the gap equations exist which allow usmore » to have a well-defined quark potential although only for unconfining'' strings of a certain length. The string tension at finite temperature for a string of various lengths is also calculated as well as [tau][sub dec][sup max] (the maximum temperature for which a tension exists) which might signal a first-order transition to a deconfined phase.« less
  • We present a complete calculation of the two-loop anomalous dimension and the corresponding Wilson coefficient for bilinear currents of heavy quarks. For momentum transfers [minus][infinity][lt][ital q][sup 2][le]([ital m][sub 1][minus][ital m][sub 2])[sup 2] our result agrees with the existing calculation of Korchemsky and Radyushkin. In addition, we give the result for the anomalous dimension and the Wilson coefficient for ([ital m][sub 1]+[ital m][sub 2])[sup 2][le][ital q][sup 2][lt][infinity].
  • We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicitymore » amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-Q{sup 2} deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1 /2 and spin-3/2 systems and find a relation useful for the analysis of the N-Delta transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.« less