We study the model for spin-$1/2$ $J_1\text{−}{J}_2$ Heisenberg antiferromagnets on a square lattice in the presence of spin vacancies. In order to overcome the methodological challenges associated with analyzing models with magnetic frustration and inhomogeneities, we introduce a new semiclassical approach in which singlet dimers are treated as effective classical degrees of freedom. The energetic and entropic aspects of the dimer formation are included via a classical Monte Carlo scheme that allows for the dynamical conversion of spin pairs into dimers and vice versa. We show that our semiclassical approach recovers the qualitative physics of the $J_1\text{−}{J}_2$ model in the absence of vacancies. The vacancies lead to a broadening of the spin-liquid regime between the Néel and the stripe antiferromagnetic phases. This suggests a possible new route to discover spin-liquid ground states by tuning the $J_2/J_1$ ratio in doped square lattice antiferromagnets.

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• Quantum spin liquid
• Mott insulators
• Quantum spin models
• Heisenberg model
• Monte Carlo methods
• Semiclassical methods