Composite fermion states on the torus

We extend the composite fermion construction to the torus geometry. We verify the validity of our construction by computing the overlap of the composite fermion state to the exact diagonalization ground state of both Coulomb interaction and Haldane-pseudopotential interaction $V_0$ ($V_1$) for bosonic (fermionic) states.

Figure 1

Overlap of CF state at filling $\nu =2/3$ for $N=10$ bosons with the exact diagonalization state using Coulomb interaction (red $\times$) and a contact interaction using the Haldane pseudopotential $V_0$ (blue $+$). The lines are a guide to the eye.

Figure 2

Overlap of CF state at filling $\nu =2/5$ for $N=6$ electrons with the exact diagonalization ground state using Coulomb interaction (red $\times$) and a short-range interaction using the Haldane pseudopotential $V_1$ (blue $+$). The lines are a guide to the eye.