Conformal Field Theory of Composite Fermions

We show that the quantum Hall wave functions for the ground states in the Jain series $\nu =n/(2np+1)$ can be exactly expressed in terms of correlation functions of local vertex operators $V_n$ corresponding to composite fermions in the $n$th composite-fermion (CF) Landau level. This allows for the powerful mathematics of conformal field theory to be applied to the successful CF phenomenology. Quasiparticle and quasihole states are expressed as correlators of anyonic operators with fractional (local) charge, allowing a simple algebraic understanding of their topological properties that are not manifest in the CF wave functions. Moreover, our construction shows how the states in the $\nu =n/(2np+1)$ Jain sequence may be interpreted as condensates of quasiparticles.

Figure 1

The density profile for the CFT state in (7) which represents two quasiparticles at $\nu =1/3$, along with the standard CF state. The total number of electrons is $N=40$. The excess charge (above the $1/3$ ground state labeled by GS) inside the disk of radius $r$ has a clear plateau at $2/3$ outside the region containing the two quasiparticles and also away from the edge. The radius $r$ is shown in units of the magnetic length and the density $\rho$ in units of the $\nu =1$ density $(2\pi l^2{)}^{-1}$.