Mott Glass Phase in the Disordered Quantum Spin Systems

We use quantum Monte Carlo method to study the disordered $S=1/2$ quantum spins on the square lattice with three different nearest neighbor interactions $J_{1}$, $J_{2}$ and $J_{3}$. Here $J_{1}$ represents weak bonds, and $J_{2}$ and $J_{3}$ correspond to stronger bonds which are randomly distributed on columnar rungs forming coupled 2-leg ladders. By tuning the average value of $J_{2}$ and $J_{3}$, the system undergoes N$\acute{e}$el-glass-paramagnetic quantum phase transition. A wide range of Mott glass phase has been found. We notice that its uniform susceptibility in the glass phase follows $ \chi\sim\exp(-b/T^{\alpha})$, where $0.5<\alpha<1$. Furthermore, this dimerized disordered quantum spin system shows the violation of Harris criterion.