Parity effects in a Luttinger liquid: Diamagnetic and paramagnetic ground states

The concept of a Luttinger liquid in 1D is extended to include twisted boundary conditions on a ring and mesoscopic parity effects due to evenness and oddness of the particle number ${\mathit{N}}_0$. Using Haldane’s notion of topological excitations, a proof of Leggett’s conjecture is presented, stating that the ground state of interacting 1D quantum systems is diamagnetic or paramagnetic depending on the parity of ${\mathit{N}}_0$. The persistent currents produced by an Aharonov-Bohm flux are calculated and shown to have period and amplitude that are in agreement with recent experiments.