Jastrow form of the Ground State Wave Functions for Fractional Quantum Hall States

Sutirtha Mukherjee; Sudhansu S Mandal

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arXiv · 1709.02070

Jastrow form of the Ground State Wave Functions for Fractional Quantum Hall States

Sutirtha Mukherjee·Sudhansu S Mandal

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Abstract

The topological morphology--order of zeros at the positions of electrons with respect to a specific electron--of Laughlin state at filling fractions $1/m$ ($m$ odd) is homogeneous as every electron feels zeros of order $m$ at the positions of other electrons. Although fairly accurate ground state wave functions for most of the other quantum Hall states in the lowest Landau level are quite well-known, it had been an open problem in expressing the ground state wave functions in terms of flux-attachment to particles, {\em a la}, this morphology of Laughlin state. With a very general consideration of flux-particle relations only, in spherical geometry, we here report a novel method for determining morphologies of these states. Based on these, we construct almost exact ground state wave-functions for the Coulomb interaction. Although the form of interaction may change the ground state wave-function, the same morphology constructs the latter irrespective of the nature of the interaction between electrons.

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Sutirtha Mukherjee, Sudhansu S Mandal. 2017-09-07. Jastrow form of the Ground State Wave Functions for Fractional Quantum Hall States. https://arxiv.org/abs/1709.02070

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