Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States

Journal Article · Fri Nov 13 04:00:00 EST 2009 · Physical Review Letters

DOI:https://doi.org/10.1103/PHYSREVLETT.103.206801· OSTI ID:21370840

Bernevig, B Andrei ^[1]; Regnault, N ^[2]

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1. Department of Physics, Princeton University, Princeton, New Jersey 08544 (United States)
2. Laboratoire Pierre Aigrain, Departement de Physique, ENS, CNRS, 24 rue Lhomond, 75005 Paris (France)

We deduce a new set of symmetries and relations between the coefficients of the expansion of Abelian and non-Abelian fractional quantum Hall (FQH) states in free (bosonic or fermionic) many-body states. Our rules allow us to build an approximation of a FQH model state with an overlap increasing with growing system size (that may sometimes reach unity) while using a fraction of the original Hilbert space. We prove these symmetries by deriving a previously unknown recursion formula for all the coefficients of the Slater expansion of the Laughlin, Read-Rezayi, and many other states (all Jacks multiplied by Vandermonde determinants), which completely removes the current need for diagonalization procedures for these model Hamiltonians.

• OSTI ID: 21370840
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 20 Vol. 103; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANATOMY
APPROXIMATIONS
BANACH SPACE
BIOLOGY
CALCULATION METHODS
EXPANSION
FERMIONS
HAMILTONIANS
HILBERT SPACE
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
QUANTUM OPERATORS
SPACE
SYMMETRY