Criticality and Mott glass phase in a disordered two-dimensional quantum spin system

Abstract

We use quantum Monte Carlo simulations to study a disordered $S=1/2$ Heisenberg quantum spin model with three different nearest-neighbor interactions, ${J}_{1}\ensuremath{\le}{J}_{2}\ensuremath{\le}{J}_{3}$, on the square lattice. We consider the regime in which ${J}_{1}$ represents weak bonds, and ${J}_{2}$ and ${J}_{3}$ correspond to two kinds of stronger bonds (dimers) which are randomly distributed on columns forming coupled two-leg ladders. When increasing the average intradimer coupling $({J}_{2}+{J}_{3})/2$, the system undergoes a N\'eel to quantum glass transition of the ground state and later a second transition into a quantum paramagnet. The quantum glass phase is of the gapless Mott glass type (i.e., in boson language it is incompressible at temperature $T=0$), and we find that the temperature dependence of the uniform magnetic susceptibility follows the stretched exponential form $\ensuremath{\chi}\ensuremath{\sim}exp(\ensuremath{-}b/{T}^{\ensuremath{\alpha}})$, with $0<\ensuremath{\alpha}<1$. At the N\'eel-glass transition, we observe the standard O(3) critical exponents, which implies that the Harris criterion for the relevance of the disorder is violated in this system.