Exact Exponents for the Spin Quantum Hall Transition in the Presence of Multiple Edge Channels

Critical properties of quantum Hall systems are affected by the presence of extra edge channels—those that are present, in particular, at higher plateau transitions. We study this phenomenon for the case of the spin quantum Hall transition. Using supersymmetry, we map the corresponding network model to a classical loop model, whose boundary critical behavior was recently determined exactly. We verify predictions of the exact solution by extensive numerical simulations.

Figure 1

Left: Network model with a bulk region of width $2L=4$, and $m=n=2$ extra channels at the left and right boundaries. Right: Schematic representation of the decomposition of average node transfer matrices. The two top rows show bulk nodes—see (6)—while the two bottom ones are boundary nodes—see (7).