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Kjall, J., Ardonne, E., Dwivedi, V., Hermanns, M. and Hansson, T. H. (2018). Matrix product state representation of quasielectron wave functions. J. Stat. Mech.-Theory Exp.. BRISTOL: IOP PUBLISHING LTD. ISSN 1742-5468

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Abstract

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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kjall, J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Ardonne, E. UNSPECIFIED UNSPECIFIED UNSPECIFIED Dwivedi, V. UNSPECIFIED UNSPECIFIED UNSPECIFIED Hermanns, M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Hansson, T. H. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-188427
DOI:	10.1088/1742-5468/aab679
Journal or Publication Title:	J. Stat. Mech.-Theory Exp.
Date:	2018
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1742-5468
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language QUANTUM HALL STATES; NON-ABELIAN STATISTICS; ONE-COMPONENT PLASMA; MANY-BODY SYSTEMS; FRACTIONAL QUANTIZATION; QUASI-PARTICLES; FIELD THEORY; RENORMALIZATION; EXCITATIONS; CONDUCTANCE Multiple languages Mechanics; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/18842