  This article provides a deeper study of the Riesz transform commutators
associated with the Neumann Laplacian operator $\Delta_N$ on $\mathbb R^n$.
Along the line of singular value estimates for Riesz transform commutators
established by Janson--Wolff and Rochberg--Semmes, we establish a full range of
Schatten-$p$ class characterization for these commutators.
