The Quantum Hall Effect of Interacting Electrons in a Periodic Potential

TL;DR

This paper investigates how an external periodic potential affects the fractional quantum Hall effect in interacting electron systems, revealing that ground state degeneracy splitting diminishes exponentially with system size and indicating phase transitions.

Contribution

It provides numerical evidence for a diverging correlation length at phase transitions from fractional to integer quantum Hall states under external potential influence.

Findings

Ground state degeneracy splitting decreases exponentially with system size.

Diverging correlation length at phase transitions.

Numerical results support continuous phase transition scenario.

Abstract

We consider the influence of an external periodic potential on the fractional quantum Hall effect of two-dimensional interacting electron systems. For many electrons on a torus, we find that the splitting of incompressible ground state degeneracies by a weak external potential diminishes as $\exp ( - L/ \xi)$ at large system size $L$. We present numerical results consistent with a scenario in which $\xi$ diverges at continuous phase transitions from fractional to integer quantum Hall states which occur with increasing external potential strength.