Evidence of a fractional quantum Hall nematic phase in a microscopic model

TL;DR

This paper provides evidence for a nematic phase in the fractional quantum Hall effect by identifying a continuous quantum phase transition from an isotropic Laughlin liquid to a nematic phase in a microscopic model, supported by numerical methods.

Contribution

It demonstrates the existence of a FQH nematic phase and characterizes the phase transition using trial wave functions and exact diagonalization in a microscopic model.

Findings

Continuous quantum phase transition between Laughlin liquid and nematic phase

Spontaneous rotational symmetry breaking in the model

Presence of stripe phase in the phase diagram

Abstract

At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in the isotropic FQH liquid. This correspondence would be exact as the GMP mode softens upon approach to the putative point of a quantum phase transition to a FQH nematic. Motivated by these considerations as well as by suggestive evidence of an FQH nematic in tilted field experiments, we have sought evidence of such a nematic FQHE in a microscopic model of interacting electrons in the lowest Landau level at filling factor 1/3. Using a family of anisotropic Laughlin states as trial wave functions, we find a continuous quantum phase transition between the isotropic Laughlin liquid and the FQH nematic. Results of numerical exact diagonalization also suggest that rotational symmetry is spontaneously broken, and that the phase diagram of the model contains both a nematic and a stripe phase.