Infinite density matrix renormalization group for multicomponent quantum Hall systems
Abstract
While the simplest quantum Hall plateaus, such as the ν=1/3 state in GaAs, can be conveniently analyzed by assuming only a single active Landau level participates, for many phases the spin, valley, bilayer, subband, or higher-Landau-level indices play an important role. These "multicomponent" problems are difficult to study using exact diagonalization because each component increases the difficulty exponentially. An important example is the plateau at ν=5/2, where scattering into higher Landau levels chooses between the competing non-Abelian Pfaffian and anti-Pfaffian states. We address the methodological issues required to apply the infinite density matrix renormalization group to quantum Hall systems with multiple components and long-range Coulomb interactions, greatly extending accessible system sizes. As an initial application we study the problem of Landau-level mixing in the ν=5/2 state. Within the approach to Landau-level mixing used here, we find that at the Coulomb point the anti-Pfaffian state is preferred over the Pfaffian state over a range of Landau-level mixing up to the experimentally relevant values.
Additional Information
© 2015 American Physical Society. Received 29 October 2014; revised manuscript received 23 December 2014; published 14 January 2015. We acknowledge J. E. Moore, C. Nayak, S. Simon, and S. Parameswaran for helpful comments and conversations. We are indebted to Z. Papíc for advice and triple checks of our data. M.P.Z. is grateful for the support of NSF Grant No. DMR-1206515; R.M. acknowledges funding from the Sherman Fairchild Foundation; E.H.R. is supported by DOE Grant No. DE-SC0002140. M.P.Z. and R.M. gratefully acknowledge support from the visitors program of the Max Planck Institute for the Physics of Complex Systems, Dresden.Attached Files
Published - PhysRevB.91.045115.pdf
Submitted - 1410.3861v2.pdf
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Additional details
- Alternative title
- Infinite DMRG for multicomponent quantum Hall systems
- Eprint ID
- 54994
- Resolver ID
- CaltechAUTHORS:20150219-091555987
- DMR-1206515
- NSF
- Sherman Fairchild Foundation
- DE-SC0002140
- Department of Energy (DOE)
- Max Planck Institute for the Physics of Complex Systems
- Created
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2015-02-20Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field