Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics
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| Format: | Preprint |
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2024
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| _version_ | 1866908048236216320 |
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| author | Shaw, Syl Römer, Rudolf A. |
| author_facet | Shaw, Syl Römer, Rudolf A. |
| contents | The real-space renormalisation group method can be applied to the Chalker-Coddington model of the quantum Hall transition to provide a convenient numerical estimation of the localisation critical exponent, $ν$. Previous such studies found $ν\sim 2.39$ which falls considerably short of the current best estimates by transfer matrix ($ν\approx 2.593$) and exact-diagonalisation studies ($ν=2.58(3)$). By increasing the amount of data $500$ fold we can now measure closer to the critical point and find an improved estimate $ν\approx 2.51$. This deviates only $\sim 3\%$ from the previous two values and is already better than the $\sim 7\%$ accuracy of the classical small-cell renormalisation approach from which our method is adapted. We also study a previously proposed mixing of the Chalker-Coddington model with a classical scattering model which is meant to provide a route to understanding why experimental estimates give a lower $ν\sim 2.3$. Upon implementing this mixing into our RG unit, we find only further increases to the value of $ν$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_00660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics Shaw, Syl Römer, Rudolf A. Disordered Systems and Neural Networks The real-space renormalisation group method can be applied to the Chalker-Coddington model of the quantum Hall transition to provide a convenient numerical estimation of the localisation critical exponent, $ν$. Previous such studies found $ν\sim 2.39$ which falls considerably short of the current best estimates by transfer matrix ($ν\approx 2.593$) and exact-diagonalisation studies ($ν=2.58(3)$). By increasing the amount of data $500$ fold we can now measure closer to the critical point and find an improved estimate $ν\approx 2.51$. This deviates only $\sim 3\%$ from the previous two values and is already better than the $\sim 7\%$ accuracy of the classical small-cell renormalisation approach from which our method is adapted. We also study a previously proposed mixing of the Chalker-Coddington model with a classical scattering model which is meant to provide a route to understanding why experimental estimates give a lower $ν\sim 2.3$. Upon implementing this mixing into our RG unit, we find only further increases to the value of $ν$. |
| title | Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2404.00660 |