Emergent composite-fermion Luttinger liquid at the half-filled Landau level

The half-filled Landau level is a fascinating point in the phase diagram of quantum Hall effect that has been hypothesized to be a non-Fermi liquid where composite-fermions (CFs) emerge at low energies. In this talk, I will present our numerical calculations of the excitation spectrum of this state on infinite cylinders. By comparing our results with a quasi-1D theory of CFs, we show compelling quantitative evidence for the emergence of a Luttinger liquid of composite-fermions at low energies, distinct from that of electrons. I will comment on some future directions.