Quantum Hall State ν = 1/3 and Antilexicographic Order of Partitions

• Authors: B. Kuśmierz , A. Wójs
• Languages of publication: EN

Abstracts

EN

We focus on a certain aspect of trial wave function approach in the fractional quantum Hall effect. We analyze the role of partition orderings and discuss the possible numerical search for the partition determining the subspace of the Hilbert space containing a particular quantum Hall wave function. This research is inspired by analogical properties of certain polynomials which are the object of interest of the symmetric function theory, especially the Jack polynomials (related to the so-called "Jack states"). Presented method may be used in the search of candidate trial wave functions. We also justify (in certain cases) diagonalization of the Coulomb repulsion Hamiltonian restricted to certain subspaces. We focus on the states at filling factor ν=1/3 in the lowest and second Landau level.

Keywords

EN

73.43.-f; 71.10.Pm; 02.10.Ox

Discipline

• 73.43.-f: Quantum Hall effects
• 71.10.Pm: Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)(for anyon mechanism in superconductors, see 74.20.Mn)
• 02.10.Ox: Combinatorics; graph theory

• Journal: Acta Physica Polonica A
• Year: 2016
• Volume: 130
• Issue: 5
• Pages: 1183-1186

Dates

published

2016-11

Contributors

author

B. Kuśmierz

• Department of Theoretical Physics, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland

author

A. Wójs

• Department of Theoretical Physics, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland

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Identifiers

DOI

10.12693/APhysPolA.130.1183