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Laughlin’s wave functions, Coulomb gases and expansions of the discriminant.(English)Zbl 0988.81563

Summary: In the context of the fractional quantum Hall effect, we investigate Laughlin’s ansatz for the ground state wave function at fractional filling of the lowest Landau level. Interpreting its normalization in terms of a one-component plasma, we find the effect of an additional quadrupolar field on the free energy, and derive estimates for the thermodynamically equivalent spherical plasma. In the second part of the paper, we present various methods for expanding the wave function in terms of Slater determinants, and obtain sum rules for the coefficients. We also address the apparently simpler question of counting the number of such Slater states using the theory of integral polytopes.

MSC:

81V70 Many-body theory; quantum Hall effect
52B11 \(n\)-dimensional polytopes
82D10 Statistical mechanics of plasmas
05E10 Combinatorial aspects of representation theory
22E70 Applications of Lie groups to the sciences; explicit representations

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