Fractional Quantum Hall Effect States as Exact Ground States

Ranjan K. Ghosh, Sumathi Rao

Published 1997-03-25, updated 1997-06-09Version 2

We construct many particle Hamiltonians for which the Laughlin and Jain wavefunctions are exact ground states. The Hamiltonians involve fermions in a magnetic field and with inter-particle interactions. For the Laughlin wave-functions,the interactions involve two- and three-body correlations similar to the Chern-Simons interactions, whereas for the projected Jain wave-functions, N-body interactions (which cannot be explicitly written down in general) are involved.