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Condensed Matter > Mesoscale and Nanoscale Physics
Title: Localization renormalization and quantum Hall systems
(Submitted on 21 Oct 2023 (v1), last revised 24 Feb 2024 (this version, v2))
Abstract: 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.
Submission history
From: Bartholomew Andrews [view email][v1] Sat, 21 Oct 2023 17:41:01 GMT (2540kb,D)
[v2] Sat, 24 Feb 2024 19:09:55 GMT (2798kb,D)
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