Emergent Dissipation in the $\nu=1$ Quantum Hall Bilayer*

Disorder is known to be central to the $\nu=1$ bilayer [1]. Building on our previous study of the bilayer $\nu=1$ system in a periodic potential [2] to capture the nonperturbative effects of disorder, we construct a $T=0$ effective theory, in which the $XY$ angle is coupled to an emergent Ising spin. We uncover a $z=2$ quantum phase transition with emergent dissipation. Calculations of the interlayer tunnelling conductance and counterflow conductivity will be presented. \\[4pt] [1] H. A. Fertig and G. Murthy, Phys. Rev. Lett. {\bf 95}, 156802 (2005). \\[0pt] [2] J. Sun, G. Murthy, H. A. Fertig, and N. Bray-Ali, Phys. Rev. B, {\bf 81}, 195314 (2010).