Symmetry breaking in Laughlin's state on a cylinder

TL;DR

This paper studies Laughlin's fractional quantum Hall wave function on a cylinder, revealing that it exhibits translational symmetry breaking in the thin-cylinder limit, with a period related to the filling factor, using polymer system analogies.

Contribution

It demonstrates symmetry breaking in Laughlin's state on a cylinder and introduces a novel proof method connecting it to polymer systems and renewal equations.

Findings

Symmetry breaking occurs in thin-cylinder Laughlin states.

The period of symmetry breaking is p times the lowest Landau level period.

The proof employs a connection to one-dimensional polymer models.

Abstract

We 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.