Exact Ensemble Average of the Random Perturbation to the Random Fixed Point

Abstract

Random scatterings among N neutral modes of the chiral Luttinger liquid can be absorbed into the random SU(N) rotations of local fields. Perturbation to the so-called random fixed point must be treated as the random perturbation. This random perturbation is characterized by random matrices with fixed eigenvalues. In this article the ensemble average of the random fixed point is obtained exactly. In the sequel, it is shown that simplifications which assume the two-sided SU(N) invariance of the random rotation lead to incorrect consequences.