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.
Highlights
One of the first non-Abelian topologically ordered candidate states was observed experimentally in 1987 [1]
We propose a unified bulk effective field theory (EFT) that gives rise to various topological quantum field theories (TQFTs) and their edge modes pertinent to the ν = 5/2 fractional quantum Hall (fQH) system
The first question to ask about our EFT equation (4) is as follows: Why do we introduce two Dirac fermions? This can be understood from solving the Bogoliubov–de Gennes (BdG) equation [15], which allows us to analyze the gap function (k, r) around the domain wall between the Pf and APf regions
Summary
One of the first non-Abelian topologically ordered candidate states was observed experimentally in 1987 [1]. It is the filling fraction ν = 5/2 fractional quantum Hall (fQH) state of an interacting electron gas in 2 + 1 space-time dimensions [denoted as (2 + 1)D]. It has a fractional quantized Hall conductance σxy = 5/2 in units of e2/h where e is the electron charge and h is the Planck constant. We first recall pertinent proposals from the literature
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