Laughlin states and their quasiparticle excitations on the torus

We provide a full derivation of Laughlin's Jastrow-type wave functions for quantized Hall states subject to periodic boundary conditions using an operator formalism. The construction includes the quasihole and the technically more challenging quasielectron excitation, which was left as an open problem in the classic paper by Haldane and Rezayi [Phys. Rev. B 31, 2529 (1985)].