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Matrix product state representation of quasielectron wave functions

Journal article
Authors J. Kjall
E. Ardonne
V. Dwivedi
Maria Hermanns
T. H. Hansson
Published in Journal of Statistical Mechanics-Theory and Experiment
Pages 60
ISSN 1742-5468
Publication year 2018
Published at Department of Physics (GU)
Pages 60
Language en
Keywords conformal field theory, fractional QHE, fractional statistics, tensor, network simulations, quantum hall states, non-abelian statistics, one-component plasma, many-body systems, fractional quantization, quasi-particles, field, theory, renormalization, excitations, conductance
Subject categories Other Physics Topics


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.

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