تقرير
Localization renormalization and quantum Hall systems
| العنوان: | Localization renormalization and quantum Hall systems |
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| المؤلفون: | Andrews, Bartholomew, Reiss, Dominic, Harper, Fenner, Roy, Rahul |
| المصدر: | Phys. Rev. B 109, 125132 (2024) |
| سنة النشر: | 2023 |
| المجموعة: | Condensed Matter |
| مصطلحات موضوعية: | Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Strongly Correlated Electrons |
| الوصف: | The obstruction to constructing localized degrees of freedom is a signature of several interesting condensed matter phases. We introduce a localization renormalization procedure that harnesses this property, and apply our method to distinguish between topological and trivial phases in quantum Hall and Chern insulators. By iteratively removing a fraction of maximally-localized orthogonal basis states, we find that the localization length in the residual Hilbert space exhibits a power-law divergence as the fraction of remaining states approaches zero, with an exponent of $\nu=0.5$. In sharp contrast, the localization length converges to a system-size-independent constant in the trivial phase. We verify this scaling using a variety of algorithms to truncate the Hilbert space, and show that it corresponds to a statistically self-similar expansion of the real-space projector. This result accords with a renormalization group picture and motivates the use of localization renormalization as a versatile numerical diagnostic for quantum Hall systems. Comment: 10+11 pages, 7+5 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevB.109.125132 |
| URL الوصول: | http://arxiv.org/abs/2310.14074 |
| رقم الأكسشن: | edsarx.2310.14074 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevB.109.125132 |
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