Possible continuous transition from fractional quantum Hall to stripe phase at $\nu_e=7/3$

TL;DR

This study reveals a continuous phase transition at filling factor 7/3 from a fractional quantum Hall state to a stripe phase driven by magnetoroton mode softening, using advanced numerical methods.

Contribution

It demonstrates a continuous transition between topologically ordered and stripe phases in the 7/3 quantum Hall state using density matrix renormalization group simulations.

Findings

Identified a continuous transition from Laughlin state to stripe phase.

Transition driven by magnetoroton mode condensation.

Stripe phase has a period of about five and a half magnetic lengths.

Abstract

We study the phase diagram of $\nu_e=7/3$ state in the $N=1$ Landau level in the presence of band mass anisotropy. Using density matrix renormalization group on an infinite cylinder geometry, we find a continuous transition from the topologically ordered Laughlin fractional quantum Hall state to a stripe phase with a period of approximately five and a half magnetic lengths. The transition is driven by the condensation of the magnetoroton mode which becomes gapless at the critical point. We interpret the transition within the composite-boson theory as the onset of stripe order in a superfluid background, resulting from the roton mode going soft.