Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States

TL;DR

This paper predicts continuous quantum phase transitions between Abelian and non-Abelian fractional quantum Hall states in two-component systems, characterized by a 3D Ising universality class and described by a Z2 gauge theory.

Contribution

It identifies a new class of continuous transitions between specific FQH states and characterizes their critical behavior with a Z2 gauged Ginzburg-Landau theory.

Findings

Transition between Halperin (p,p,p-3) and Z4 parafermion states is continuous.

Critical point belongs to the 3D Ising universality class.

Implications for experiments at 0/3 and 8/3 filling fractions.

Abstract

We find a series of possible continuous quantum phase transitions between fractional quantum Hall (FQH) states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at \nu = 2/3 and single-component systems at \nu = 8/3.