XY* Transition and Extraordinary Boundary Criticality from Fractional Exciton Condensation in Quantum Hall Bilayer

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) 1/4 (13 , 23) 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 a 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 interlayer tunneling and counterflow transport, respectively. We also show that the edge is likely to realize the newly predicted extraordinary log 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. The XY* critical theory can be generalized to a bilayer system with an arbitrary Abelian state in one layer and its particle-hole partner in the other layer. Therefore, we anticipate many distinct XY* transitions corresponding to the different Laughlin states and Jain sequences in the single-layer case.