We employ the stochastic series expansion quantum Monte Carlo method to investigate the $S=1/2$ antiferromagnetic Heisenberg model on a bilayer square lattice with diluted interlayer couplings. Both regular and random dilution patterns are considered. In systems with regular dilution, tuning the interlayer interaction drives a quantum phase transition from a Néel-ordered phase to a quantum disordered phase, consistent with the $O\left(3\right)$ universality class. In contrast, random dilution gives rise to a two-step transition: from the Néel phase to an intermediate Mott glass (MG) phase, followed by a transition to the quantum disordered phase. Within the MG phase, the uniform magnetic susceptibility exhibits a stretched-exponential temperature dependence ${\chi }_u\sim exp(-b/T^{\alpha }), 0<\alpha <1$. At the Néel-to-glass transition, the quenched disorder modifies the critical exponents in a manner consistent with the Harris criterion. These findings provide new insights into disorder-driven quantum phase transitions and the emergence of glassy phases in diluted bilayer quantum magnets.

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• Antiferromagnetism
• Exchange interaction
• Magnetism
• Quantum criticality
• Quantum phase transitions
• 2-dimensional systems
• Heisenberg model
• Quantum Monte Carlo