Detecting confinement-deconfinement phase transition in disorder toric code using Spectrum Bifurcation Renormalization Group

Randomness is common in nature and it could quantitatively change the behavior of the system, and critical universality class. Here, we generalize the spectrum bifurcation renormalization group (SBRG) method to the two dimensional strong disorder system. We first numerically calculated 2D Ising model in the strong disorder limit, and we find the phase transition point and critical exponent are consistent with the previous strong disorder renormalization group calculation. Next, we applied our method to the 2D toric code model in strong disorder limit. We showed that long range mutual information can be served as an indicator of the confinement-deconfinement phase transition.