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Matrix product state representation of quasielectron wave functions
Stockholm Univ, AlbaNova Univ Ctr, Dept Phys, SE-10691 Stockholm, Sweden..
Stockholm Univ, AlbaNova Univ Ctr, Dept Phys, SE-10691 Stockholm, Sweden..
Univ Cologne, Inst Theoret Phys, D-50937 Cologne, Germany..
Univ Cologne, Inst Theoret Phys, D-50937 Cologne, Germany.;Univ Gothenburg, Dept Phys, SE-41296 Gothenburg, Sweden..
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2018 (English)In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 053101Article in journal (Refereed) Published
Abstract [en]

Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.

Place, publisher, year, edition, pages
IOP PUBLISHING LTD , 2018. article id 053101
Keywords [en]
conformal field theory, fractional QHE, fractional statistics, tensor network simulations
National Category
Computer and Information Sciences
Identifiers
URN: urn:nbn:se:kth:diva-227738DOI: 10.1088/1742-5468/aab679ISI: 000431316600001Scopus ID: 2-s2.0-85048062237OAI: oai:DiVA.org:kth-227738DiVA, id: diva2:1205746
Funder
Swedish Research Council
Note

QC 20180515

Available from: 2018-05-15 Created: 2018-05-15 Last updated: 2018-10-16Bibliographically approved

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