An Effective Field Theory for Fractional Quantum Hall Systems near $\nu=5/2$

TL;DR

This paper develops an effective field theory for fractional quantum Hall systems near filling fraction 5/2, capturing various candidate phases, phase transitions, and domain wall properties, advancing understanding of topological quantum states.

Contribution

It introduces a novel EFT model that describes multiple phases and transitions in fractional quantum Hall systems near ν=5/2, including non-abelian states and domain wall dynamics.

Findings

Reproduces phase diagram with tunable parameters.

Captures features of domain walls between different phases.

Predicts domain wall tension hierarchy and transition pathways.

Abstract

We propose an effective field theory (EFT) of fractional quantum Hall systems near the filling fraction $\nu=5/2$ that flows to pertinent IR candidate phases, including non-abelian Pfaffian, anti-Pfaffian, and particle-hole Pfaffian states (Pf, APf, and PHPf). Our EFT has a 2+1$d$ O(2)$_{2,L}$ Chern-Simons gauge theory coupled to four Majorana fermions by a discrete charge conjugation gauge field, with Gross-Neveu-Yukawa-Higgs terms. Including deformations via a Higgs condensate and fermion mass terms, we can map out a phase diagram with tunable parameters, reproducing the prediction of the recently-proposed percolation picture and its gapless topological quantum phase transitions. Our EFT captures known features of both gapless and gapped sectors of time-reversal-breaking domain walls between Pf and APf phases. Moreover, we find that Pf$\mid$APf domain walls have higher tension than domain walls in the PHPf phase. Then the former, if formed, may transition to the energetically-favored PHPf domain walls; this could, in turn, help further induce a bulk transition to PHPf.