Title: Composite Fermions on a Torus,
Abstract: We achieve an explicit construction of the lowest Landau level (LLL)
projected wave functions for composite fermions in the periodic (torus)
geometry. To this end, we first demonstrate how the vortex attachment of the
composite fermion (CF) theory can be accomplished in the torus geometry to
produce the "unprojected" wave functions satisfying the correct
(quasi-)periodic boundary conditions. We then consider two methods for
projecting these wave functions into the LLL. The direct projection produces
valid wave functions but can be implemented only for very small systems. The
more powerful and more useful projection method of Jain and Kamilla fails in
the torus geometry because it does not preserve the periodic boundary
conditions and thus takes us out of the original Hilbert space. We have
succeeded in constructing a modified projection method that is consistent with
both the periodic boundary conditions and the general structure of the CF
theory. This method is valid for a large class of states of composite fermions,
called "proper states," which includes the incompressible ground states at
electron filling factors $\nu=\frac{n}{2pn+ 1}$, their charged and neutral
excitations, and also the quasidegenerate ground states at arbitrary filling
factors of the form $\nu=\frac{\nu^*}{2p\nu^*+ 1}$, where $n$ and $p$ are
integers and $\nu^*$ is the CF filling factor. Comparison with exact results
known for small systems for the ground and excited states at filling factors
$\nu=1/3$, 2/5 and 3/7 demonstrates our LLL-projected wave functions to be
extremely accurate representations of the actual Coulomb eigenstates. Our
construction enables the study of large systems of composite fermions on the
torus, thereby opening the possibility of investigating numerous interesting
questions and phenomena.