Fractional Quantum Hall Effect States as Exact Ground States

TL;DR

This paper constructs specific many-particle Hamiltonians with interactions tailored so that Laughlin and Jain wavefunctions are their exact ground states, advancing understanding of fractional quantum Hall states.

Contribution

It introduces explicit Hamiltonians involving multi-body interactions that exactly realize Laughlin and Jain wavefunctions as ground states.

Findings

Laughlin wavefunctions are ground states of Hamiltonians with two- and three-body interactions.

Jain wavefunctions are ground states of Hamiltonians involving N-body interactions.

The work links wavefunctions to specific interaction Hamiltonians in fractional quantum Hall systems.

Abstract

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.