Anyons and fractional quantum Hall effect in fractal dimensions

Sourav Manna, Biplab Pal, Wei Wang, Anne E.B. Nielsen

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal dimensions. We provide analytical wave functions and exact few-body parent Hamiltonians, and we show numerically for several different Hausdorff dimensions between 1 and 2 that the systems host anyons. We also find examples of fractional quantum Hall physics in fractals with Hausdorff dimension 1 and ln(4)/ln(5). Our results suggest that the local structure of the investigated fractals is more important than the Hausdorff dimension to determine whether the systems are in the desired topological phase. The study paves the way for further investigations of strongly correlated topological systems in fractal dimensions.

Original languageEnglish
Article number023401
JournalPhysical Review Research
Issue number2
StatePublished - 25 Jun 2020
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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