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Title: Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
Authors: Wang, Yuzhu
Yang, Bo
Keywords: Science::Physics
Issue Date: 2022
Source: Wang, Y. & Yang, B. (2022). Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications. Physical Review B, 105(3), 035144-.
Project: NRF-NRFF12-2020-0005
NTU SUG grant 
Journal: Physical Review B
Abstract: Neutral excitations in a fractional quantum Hall droplet define the incompressibility gap of the topological phase. In this paper, we derive a set of analytical results for the energy gap of the graviton modes with two-body and three-body Hamiltonians in both the long-wavelength and the thermodynamic limit. These allow us to construct model Hamiltonians for the graviton modes in different FQH phases, and to elucidate a hierarchical structure of conformal Hilbert spaces (null spaces of model Hamiltonians) with respect to the graviton modes and their corresponding ground states. Using the analytical tools developed, we perform numerical analysis with a particular focus on the Laughlin ν=1/5 and the Gaffnian ν=2/5 phases. Our calculation shows that for gapped phases, low-lying neutral excitations can undergo a "phase transition"even when the ground state is invariant. We discuss the compressibility of the Gaffnian phase, the possibility of multiple graviton modes, and the transition from the graviton modes to the "hollow-core"modes, as well as their experimental consequences.
ISSN: 2469-9950
DOI: 10.1103/PhysRevB.105.035144
Rights: © 2022 American Physical Society. All rights reserved. This paper was published in Physical Review B and is made available with permission of American Physical Society.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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