2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212913We investigate Laughlin's fractional quantum Hall effect wave function on a cylinder. We show that it displays translational symmetry breaking in the axial direction for sufficiently thin cylinders. At filling factor 1/p, the period is p times the period of the filled lowest Landau level. The proof uses a connection with one-dimensional polymer systems and discrete renewal equations.34 pages, 5 figures. A few explanations addedMesoscale and Nanoscale PhysicsMathematical Physicstext