Relevant perturbations at the spin quantum Hall transition

We study relevant perturbations at the spin quantum Hall critical point using a network model formulation. The model has been previously mapped to classical percolation on a square lattice, and we use the mapping to extract exact analytical values of the scaling dimensions of the relevant perturbations. We find that several perturbations that are distinct in the network model formulation correspond to the same operator in the percolation picture. We confirm our analytical results by comparing them with numerical simulations of the network model.

Figure 1

Two-channel chiral network model. Dots represent scattering matrices on the links (1) and squares represent the nodal scattering matrices (2).

Figure 2

The scattering amplitudes at the nodes on the two sublattices. The node scattering matrices are diagonal in the spin indices, so we only show one channel per link.

Figure 3

Deviation from Kramer's degeneracy as function of $p{M}^{1/{\mu }_p}$ with ${\mu }_p=1.15$ for $\epsilon =\Delta =0$.

Figure 4

Schematic plot of the phase boundary $\epsilon =\pm {(a{\Delta }^2+b{p}^2)}^{\phi /2}$.

Figure 5

The weights of the adjoint representation of $\mathfrak{osp}\left(2\right|2)$. We show two doublets and the adjoint of the subalgebra $\mathfrak{gl}\left(1\right|1)$.

Figure 6

The weights of the fundamental representation $\pi (\frac{1}{2},\frac{1}{2})$ of $\mathfrak{osp}\left(2\right|2)$ and its dual $\pi (-\frac{1}{2},\frac{1}{2})$.