Yang, B, Wu, Y-H and Papic, Z orcid.org/0000-0002-8451-2235 (2019) Effective Abelian theory from a non-Abelian topological order in the ν = 2/5 fractional quantum Hall effect. Physical Review B: Condensed Matter and Materials Physics, 100 (24). 245303. ISSN 1098-0121
Abstract
Topological phases of matter are distinguished by topological invariants, such as Chern numbers and topological spins, that quantize their response to electromagnetic currents and changes of ambient geometry. Intriguingly, in the ν=2/5 fractional quantum Hall effect, prominent theoretical approaches—the composite fermion theory and conformal field theory—have constructed two distinct states, the Jain composite fermion (CF) state and the Gaffnian state, for which many of the topological indices coincide and even the microscopic ground-state wave functions have high overlap with each other in system sizes accessible to numerics. At the same time, some aspects of these states are expected to be very different; e.g., their elementary excitations should have either Abelian (CF) or non-Abelian (Gaffnian) statistics. In this paper we investigate the close relationship between these two states by considering not only their ground states, but also the low-energy charged excitations. We show that the low-energy physics of both phases is spanned by the same type of quasielectrons of the neighboring Laughlin phase. The main difference between the two states arises due to an implicit assumption of short-range interaction in the CF approach, which causes a large splitting of the variational energies of the Gaffnian excitations. We thus propose that the Jain phase emerges as an effective Abelian low-energy description of the Gaffnian phase when the Hamiltonian is dominated by two-body interactions of sufficiently short range.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 American Physical Society. This is an author produced version of a journal article accepted for publication in Physical Review B. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/R020612/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Dec 2019 15:58 |
Last Modified: | 16 Jan 2020 15:44 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevB.100.245303 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:154281 |