Composite-fermion wave functions as correlators in conformal field theory

• It is known that a subset of fractional quantum Hall wave functions has been expressed as conformal field theory (CFT) correlators, notably the Laughlin wave function [Phys. Rev. Lett. 50, 1395 (1983)] at filling factor nu=1/m (m odd) and its quasiholes, and the Pfaffian wave function at nu=1/2 and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at nu=1/m are created by inserting anyonic vertex operators, P-1/m(z), that replace a subset of the electron operators in the correlator. The one-quasiparticle wave function is identical to the corresponding CF wave function, and the two-quasiparticle wave function has correct fractional charge and statistics and is numerically almost identical to the corresponding CF wave function. We further show how to exactly represent the CF wave functions in the Jain series nu=s/(2sp+1) [Phys. Rev. Lett. 63, 199 (1989); Composite Fermions (Cambridge University Press, Cambridge, 2007)] as the CFT correlators of a new type of fermionic vertex operators, V-p,V-n(z), constructed from n free compactified bosons; these operators provide the CFT representation of composite fermions carrying 2p flux quanta in the nth CF Landau level. We also construct the corresponding quasiparticle and quasihole operators and argue that they have the expected fractional charge and statistics. For filling fractions 2/5 and 3/7, we show that the chiral CFTs that describe the bulk wave functions are identical to those given by Wen's general classification [Int. J. Mod. Phys. B 6, 1711 (1992); Adv. Phys. 44, 405 (1995)] of quantum Hall states in terms of K matrices and l and t vectors, and we propose that to be generally true. Our results suggest a general procedure for constructing quasiparticle wave functions for other fractional Hall states, as well as for constructing ground states at filling fractions not contained in the principal Jain series.

Ämnesord

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Nyckelord

quantum hall states

quasi-particles

statistics

charge

construction

excitations

solitons

systems

order

edge

Physics

Fysik

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