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    Energy projection and modified Laughlin states


    Fremling, M. and Fulsebakke, Jorgen and Moran, N. and Slingerland, Joost (2016) Energy projection and modified Laughlin states. Physical Review B, 93 (235149). ISSN 1098-0121

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    Abstract

    We develop a method to efficiently calculate trial wave functions for quantum Hall systems which involve projection onto the lowest Landau level. The method essentially replaces the lowest Landau level projection by projection onto the M lowest eigenstates of a suitably chosen Hamiltonian acting within the lowest Landau level. The resulting “energy projection” is a controlled approximation to the exact lowest Landau level projection which improves with increasing M. It allows us to study the projected trial wave functions for system sizes close to the maximal sizes that can be reached by exact diagonalization and can be straightforwardly applied in any geometry. As a first application and test case, we study a class of trial wave functions first proposed by Girvin and Jach [Girvin and Jach, Phys. Rev. B 29, 5617 (1984)], which are modifications of the Laughlin states involving a single real parameter. While these modified Laughlin states probably represent the same universality class exemplified by the Laughlin wave functions, we show by extensive numerical work for systems on the sphere and torus that they provide a significant improvement of the variational energy, overlap with the exact wave function and properties of the entanglement spectrum.

    Item Type: Article
    Additional Information: We thank Hans Hansson for pointing us in the direction of the modified Laughlin wave functions and Steve Simon and Andrei Bernevig for useful discussions. J.K.S. thanks Nordita for its hospitality during the program on Physics of Interfaces and Layered Structures (2015), when part of this work was done. N.M. thanks the organisers of the TOPO2015 workshop held at the Institut d’Etudes Scientifiques de Carg`ese where part of this work and related discussions took place. All authors acknowledge financial support through SFI Principal Investigator Award 12/IA/1697.We also wish to acknowledge the SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities and support.
    Keywords: Fractional quantum Hall effect; Quantum Hall effect; 2-dimensional systems; Conformal field theory; Numerical approximation & analysis; Variational approach;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 10533
    Identification Number: https://doi.org/10.1103/PhysRevB.93.235149
    Depositing User: Dr. Joost Slingerland
    Date Deposited: 21 Feb 2019 12:13
    Journal or Publication Title: Physical Review B
    Publisher: American Physical Society
    Refereed: Yes
    Funders: Science Foundation Ireland (SFI)
    URI:

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