  The phase diagram of Kane-Mele-Heisenberg (KMH) model in classical
limit~\cite{zare}, contains disordered regions in the coupling space, as the
result of to competition among different terms in the Hamiltonian, leading to
frustration in finding a unique ground state. In this work we explore the
nature of these phase in the quantum limit, for a $S=1/2$. Employing exact
diagonalization (ED) in $S_z$ and nearest neighbor valence bond (NNVB) bases,
bond and plaquette valence bond mean field theories, We show that the
disordered regions are divided into ordered quantum states in the form of
plaquette valence bond crystal(PVBC) and staggered dimerized (SD) phases.

Strongly Correlated Electrons