Competing Abelian and non-Abelian topological orders in ν = 1/3+1/3 quantum Hall bilayers
Abstract
Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two subbands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν=1/3+1/3. We first consider the Coulomb interaction at bilayer separation d, bilayer tunneling energy Δ_(SAS), and individual layer width w, where we find a phase diagram which includes three competing Abelian phases: a bilayer Laughlin phase (two nearly decoupled ν=1/3 layers), a bilayer spin-singlet phase, and a bilayer symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases has also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν=1/3+1/3 systems merit further experimental study.
Additional Information
© 2015 American Physical Society. Received 21 February 2015; revised manuscript received 8 May 2015; published 27 May 2015. We acknowledge helpful conversations with Jason Alicea, Eddy Ardonne, Maissam Barkeshli, Parsa Bonderson, and Xiaoliang Qi. We are particularly grateful to Jim Eisenstein, without whom this work would not have been started. S.G. is supported by the National Science Engineering Research Council (NSERC) of Canada. M.Z. is indebted to the David & Lucile Packard Foundation. Z.P. acknowledges support by DOE Grant No. DE-SC0002140. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation. R.M. acknowledges the Sherman Fairchild Foundation for support.Attached Files
Published - PhysRevB.91.205139.pdf
Submitted - 1502.01340v1.pdf
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Additional details
- Eprint ID
- 57187
- Resolver ID
- CaltechAUTHORS:20150504-102529982
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- David and Lucile Packard Foundation
- DE-SC0002140
- Department of Energy (DOE)
- Government of Canada Industry Canada
- Sherman Fairchild Foundation
- Province of Ontario Ministry of Economic Development and Innovation
- Created
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2015-05-04Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field