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In this work, we prove a bound on multiplicity of the singular spectrum forcertain class of Anderson Hamiltonians. The class of operator is$H^\omega=\Delta+\sum_{n\in\mathbb{Z}^d}\omega_n P_n$ on the Hilbert space$\ell^2(\mathbb{Z}^d)$, where $\Delta$ is discrete laplacian, $P_n$ areprojection onto $\ell^2(\{x\in\mathbb{Z}^d:n_il_i<x_i\leq (n_i+1)l_i\})$ forsome $l_1,\cdots,l_d\in\mathbb{N}$ and $\{\omega_n\}_n$ are i.i.d real boundedrandom variables following absolutely continuous distribution. We prove thatthe multiplicity of singular spectrum is bounded above by $2^d-d$ independentof $\{l_i\}_{i=1}^d$. When $l_i+1\not\in 2\mathbb{N}\cup3\mathbb{N}$ for all$i$ and $gcd(l_i+1,l_j+1)=1$ for $i\neq j$, we also prove that the singularspectrum is simple.

Multiplicity bound of Singular Spectrum for higher rank Anderson models