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Title: Gaffnian and Haffnian : physical relevance of nonunitary conformal field theory for the incompressible fractional quantum Hall effect
Authors: Yang, Bo
Keywords: Science::Physics
Issue Date: 2021
Source: Yang, B. (2021). Gaffnian and Haffnian : physical relevance of nonunitary conformal field theory for the incompressible fractional quantum Hall effect. Physical Review B, 103, 115102-1-115102-16.
Project: NRF- NRFF12-2020-0005
Journal: Physical Review B 
Abstract: We motivate a close look on the usefulness of the Gaffnian and Haffnian quasihole manifold (null spaces of the respective model Hamiltonians) for well-known gapped fractional quantum Hall phases. The conformal invariance of these subspaces is derived explicitly from microscopic many-body states. The resultant conformal field theory (CFT) description leads to an intriguing emergent primary field with h = 2, c = 0, and we argue the quasihole manifolds are quantum mechanically well defined and well behaved. Focusing on the incompressible phases at ν = 1/3 and 2/5, we show the low-lying excitations of the Laughlin phase are quantum fluids of Gaffnian and Haffnian quasiholes, and give a microscopic argument showing that the Haffnian model Hamiltonian is gapless against Laughlin quasielectrons. We discuss the thermal Hall conductance and shot-noise measurements at ν = 2/5, and argue that the experimental observations can be understood from the dynamics within the Gaffnian quasihole manifold. A number of detailed predictions on these experimental measurements are proposed, and we discuss their relationships to the conventional CFT arguments and the composite fermion descriptions.
ISSN: 2469-9969
DOI: 10.1103/PhysRevB.103.115102
Rights: © 2021 American Physical Society (APS). All rights reserved. This paper was published in Physical Review B and is made available with permission of American Physical Society (APS).
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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