Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states

Abstract

We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences. By a generalized ``flux attachment" construction we extend the Ginzburg-Landau-Chern-Simons composite boson theory to states obtained by both quasielectron and quasihole condensation, and express the corresponding wave functions as correlators in conformal field theories. This yields a precise identification of the relativistic scalar fields entering these correlators in terms of the original electron field.

Adiabatic construction of hierarchical quantum Hall states

“…Introduction. The adiabatic principle for quantized Hall states [1] asserts that such states at different Landau filling fractions [2][3][4][5][6][7][8][9][10][11][12] can be obtained from each other through a process of adiabatic localization of magnetic flux onto the particles [13][14][15][16][17]. Using an exactly solvable model of anyons [18][19][20][21], we have previously [22] been able to interpolate continuously between a filled Landau level and Laughlin 1/m states [2], as well as a p-wave superfluid and a Pfaffian state at Landau-level filling fraction ν = 1 2 [23][24][25][26][27][28][29][30][31][32][33][34].…”

Mean Field Theories of Quantum Hall Liquids Justified: Variations on the Greiter Wilczek Theme

“…The physical meaning of this is that the electrons carry different orbital spins 18 , and this must be incorporated in the composite boson picture. How to do this was shown in a recent paper 19 , which however also relied on a mean filed approximation.…”

Adiabatic Construction of Hierarchical Quantum Hall States

“…Introduction.-The adiabatic principle for quantized Hall states [1] asserts that such states at different Landau filling fractions [2][3][4][5][6][7][8][9][10][11][12] can be obtained from each other through a process of adiabatic localization of magnetic flux onto the particles [13][14][15][16][17]. Using an exactly solvable model of anyons [18][19][20], we have previously [21] been able to interpolate continuously between a filled Landau level and Laughlin 1/m states [2], as well as a p-wave superfluid and a Pfaffian state at Landau level filling fraction ν = 1 2 [22][23][24][25][26][27][28][29][30][31][32][33].…”

“…The factor (eB) p−1 in the denominator ensures that H (θ) p has the correct units. To verify that ( 23) is a zero energy ground state, we note that H (θ) p is positive semi-definite, and use (11) and (12) to rewrite it as…”