Finite-size effects and irrelevant corrections to scaling near the integer quantum Hall transition
We present a numerical finite-size scaling study of the localization length in long cylinders near the integer quantum Hall transition employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical...
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| Published in: | Physical review letters Vol. 109; no. 20; p. 206804 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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16-11-2012
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| Abstract | We present a numerical finite-size scaling study of the localization length in long cylinders near the integer quantum Hall transition employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent y is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate |y|>/~0.4, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent 2.62±0.06 confirming recent results. Our stability analysis has broad applicability to other observables at integer quantum Hall transition, as well as other critical points where corrections to scaling are present. |
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| AbstractList | We present a numerical finite-size scaling study of the localization length in long cylinders near the integer quantum Hall transition employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent y is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate |y|>/~0.4, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent 2.62±0.06 confirming recent results. Our stability analysis has broad applicability to other observables at integer quantum Hall transition, as well as other critical points where corrections to scaling are present. We present a numerical finite-size scaling study of the localization length in long cylinders near the integer quantum Hall transition employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent y is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate |y|>/~0.4, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent 2.62±0.06 confirming recent results. Our stability analysis has broad applicability to other observables at integer quantum Hall transition, as well as other critical points where corrections to scaling are present. |
| ArticleNumber | 206804 |
| Author | Gruzberg, Ilya A Evers, Ferdinand Obuse, Hideaki |
| Author_xml | – sequence: 1 givenname: Hideaki surname: Obuse fullname: Obuse, Hideaki organization: Institute of Nanotechnology, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany – sequence: 2 givenname: Ilya A surname: Gruzberg fullname: Gruzberg, Ilya A – sequence: 3 givenname: Ferdinand surname: Evers fullname: Evers, Ferdinand |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/23215518$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1103/PhysRevB.64.241303 10.1142/S021797929400049X 10.1103/PhysRevLett.76.4207 10.1007/BF01578242 10.1103/PhysRevLett.101.116802 10.1016/j.physrep.2005.07.001 10.1103/PhysRevB.84.245447 10.1103/RevModPhys.80.1355 10.1103/PhysRevLett.82.3516 10.1103/PhysRevLett.105.046403 10.1103/RevModPhys.67.357 10.1103/PhysRevLett.82.382 10.1103/PhysRevB.70.045309 10.1016/S0370-1573(97)00050-1 10.1016/j.physleta.2006.03.075 10.1103/PhysRevLett.89.256601 10.1103/PhysRevB.86.165324 10.1103/PhysRevLett.107.066402 10.1103/PhysRevB.84.115133 10.1103/PhysRevLett.101.116803 10.1103/PhysRevB.82.035309 10.1103/PhysRevLett.107.086403 10.1103/PhysRevLett.90.056804 10.1016/j.physletb.2007.08.022 10.1103/PhysRevB.75.184201 10.1103/PhysRevB.84.134209 10.1103/PhysRevLett.108.126801 10.1103/PhysRevB.70.035115 10.1103/PhysRevLett.101.256802 10.1016/S0550-3213(00)00276-5 10.1142/S2010194512006162 10.1016/j.nuclphysb.2011.04.020 10.1103/PhysRevB.80.041304 10.1088/0022-3719/21/14/008 |
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