Success and failure of the plasma analogy for Laughlin states on a torus

We investigate the nature of the plasma analogy for the Laughlin wave function on a torus describing the quantum Hall plateau at nu = 1/q. We first establish, as expected, that the plasma is screening if there are no short nontrivial paths around the torus. We also find that when one of the handles has a short circumference-i.e. the thin-torus limit-the plasma no longer screens. To quantify this we compute the normalization of the Laughlin state, both numerically and analytically. In the thin torus limit, the analytical form of the normalization simplify and we can reconstruct the normalization and analytically extend it back into the 2D regime. We find that there are geometry dependent corrections to the normalization, and this in turn implies that the plasma in the plasma analogy is not screening when in the thin torus limit. Despite the breaking of the plasma analogy in this limit, the analytical approximation is still a good description of the normalization for all tori, and also allows us to compute hall viscosity at intermediate thickness.