Many-particle exchanges in a class of correlated Gaussian wave functions for the fractionally quantized Hall effect

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Abstract
The many-particle exchange integral for a class of correlated Gaussian wave functions for the fractionally quantized Hall effect are discussed. When the correlation is of a long-range nature, the evaluation of this exchange can be cast into languages involving the study of the energies and fluctuations of grain boundaries in two dimensions. For a class of trial wave functions studied recently by Chui, Ma, and Hakim, exchanges involving a large number of particles are significant in that, for a loop that consists of two long parallel boundaries, the overlap integral actually increases as the number of particles involved in the exchange is increased. The question of a collection of boundaries is discussed. We find that there is a repulsion between the boundaries of a range proportional to the size of the boundary.