Topological Characterization of Fractional Quantum Hall Ground States from Microscopic Hamiltonians
Abstract
We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall Hamiltonian. To find the set of degenerate ground states, we employ the infinite density matrix renormalization group method based on the matrix-product state representation of fractional quantum Hall states on an infinite cylinder. To study localized quasiparticles of a chosen topological charge, we use pairs of degenerate ground states as boundary conditions for the infinite density matrix renormalization group. We then show that the wave function obtained on the infinite cylinder geometry can be adapted to a torus of arbitrary modular parameter, which allows us to explicitly calculate the non-Abelian Berry connection associated with the modular T transformation. As a result, the quantum dimensions, topological spins, quasiparticle charges, chiral central charge, and Hall viscosity of the phase can be obtained using data contained entirely in the entanglement spectrum of an infinite cylinder.
Additional Information
© 2013 American Physical Society. Received 20 December 2012; published 4 June 2013. We thank L. Fidkowski, T. Grover, S. Parameswaran, A. Turner, N. Read, and J. Moore for useful discussions. We are grateful to J. Bárðarson for comments on the manuscript. M. P. Z. acknowledges the hospitality of the guest program of MPI-PKS Dresden and support from NSF GRFP Grant No. DGE 1106400. R. S.K.M. is supported by NSF Grant No. DMR-0804413 and the Sherman Fairchild Foundation.Attached Files
Published - PhysRevLett.110.236801.pdf
Submitted - 1211.3733v3.pdf
Supplemental Material - README.TXT
Supplemental Material - supplemental.pdf
Files
Additional details
- Eprint ID
- 39442
- Resolver ID
- CaltechAUTHORS:20130718-103242140
- DGE 1106400
- NSF Graduate Research Fellowship Program (GRFP)
- DMR-0804413
- NSF
- Sherman Fairchild Foundation
- Created
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2013-07-22Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field