Few-body treatment of the quantum Hall system

When confined to a finite, two-dimensional area and exposed to a strong magnetic field, fermions exhibit complicated, highly-correlated quantum behavior known as the quantum Hall effect [1]. At certain electron densities and magnetic fields, the system exhibits strong quantization due entirely to Coulomb interactions. Typical theoretical studies in the field consist of many-body numerical configuration interaction calculations performed in an energy-restricted single-particle Hilbert subspace. So far, quantum Hall behavior has been observed experimentally only in condensed matter systems, but there is significant interest in reproducing and studying the effect in highly-controlled cold atom systems. In light of such potential experimental developments, we approach the theoretical study of the quantum Hall system from a few-body perspective using the hyperspherical adiabatic technique [2] developed originally for atomic systems.\\[4pt] [1] D. C.~Tsui, H. L.~Stormer, and A. C.~Gossard, Phys.\ Rev.\ Lett. \textbf{48}, 1559 (1982).\\[0pt] [2] J.~Macek, J.\ Phys.\ B:.\ At.\ Mol.\ Phys., {\bf 1} 831 (1968).