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Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian

Mishmash, Ryan V. and Mross, David F. and Alicea, Jason and Motrunich, Olexei I. (2018) Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian. Physical Review B, 98 (8). Art. No. 081107. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20180810-093237801

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Abstract

We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian (“PH-Pfaffian”) topological order, a phase consistent with the recently reported thermal Hall conductance [M. Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic ν = 5/2 quantum Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial state performs reasonably well energetically in the half-filled lowest Landau level, but is likely not a good starting point for understanding the ν = 5/2 ground state. Our results suggest that the PH-Pfaffian model wave function either encodes anomalously weak p-wave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.98.081107DOIArticle
https://arxiv.org/abs/1804.01107arXivDiscussion Paper
ORCID:
AuthorORCID
Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:© 2018 American Physical Society. Received 12 April 2018; revised manuscript received 19 June 2018; published 10 August 2018. R.V.M. gratefully acknowledges Mike Zaletel for valuable discussions; we thank Ajit Balram for pointing out the connection between the α = 2 generalized PH-Pfaffian state and the states proposed in Ref. [73]. This work was supported by Grant No. 2016258 from the United States-Israel Binational Science Foundation (BSF); the Minerva foundation with funding from the Federal German Ministry for Education and Research (D.F.M.); the Army Research Office under Grant Award No. W911NF-17-1-0323 (J.A.); the NSF through Grants No. DMR-1723367 (J.A.) and No. DMR-1619696 (O.I.M.); the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant GBMF1250; and the Walter Burke Institute for Theoretical Physics at Caltech.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)2016258
Minerva FoundationUNSPECIFIED
Bundesministerium für Bildung und Forschung (BMBF)UNSPECIFIED
Army Research Office (ARO)W911NF-17-1-0323
NSFDMR-1723367
NSFDMR-1619696
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechAUTHORS:20180810-093237801
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180810-093237801
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88747
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Aug 2018 15:35
Last Modified:13 Aug 2018 15:35

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