XY* transition and extraordinary boundary criticality from fractional exciton condensation in quantum Hall bilayer

Abstract

XY* transitions represent one of the simplest examples of unconventional quantum criticality, in which fractionally charged excitations condense into a superfluid, and display novel features that combine quantum criticality and fractionalization. Nevertheless their experimental realization is challenging. Here we propose to study the XY* transition in quantum Hall bilayers at filling $({\nu }_1,{\nu }_2)=(\frac{1}{3},\frac{2}{3})$ where the exciton condensate (EC) phase plays the role of the superfluid. Supported by exact diagonalization calculation, we argue that there is a continuous transition between an EC phase at small bilayer separation to a pair of decoupled fractional quantum Hall states, at large separation. The transition is driven by condensation of a fractional exciton, a bound state of Laughlin quasiparticle and quasihole, and is in the XY* universality class. The fractionalization is manifested by unusual properties including a large anomalous exponent and fractional universal conductivity, which can be conveniently measured through inter-layer tunneling and counter-flow transport, respectively. We also show that the edge is likely to realize the newly predicted extra-ordinary boundary criticality. Our work highlights the promise of quantum Hall bilayers as an ideal platform for exploring exotic bulk and boundary critical behaviors, that are amenable to immediate experimental exploration in dual-gated bilayer systems.

arXiv comment5+7 pages; 3 figures; v2: add a section on general Abelian states; also add some references

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• Notes on a Surface Defect in the $O(N)$ Model
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Critical relaxational dynamics at the continuous transitions of three-dimensional spin models with ${\mathbb{Z}}_2$ gauge symmetry
• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)${}^{\ast }$ and Ising${}^{\ast }$ continuous transitions
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Exciton Condensation in Landau Levels of Quantum Spin Hall Insulators
• Single-parameter variational wavefunctions for quantum Hall bilayers
• Topological spin-up triplet excitonic condensation in two-dimensional electron-hole systems
• Boundary critical behavior of the Gross-Neveu-Yukawa model
• Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter