Motivated by the experimental observation of a nonmagnetic phase in compounds with frustration and disorder, we study the ground state of a spin-$1/2$ square-lattice Heisenberg model with randomly distributed nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ couplings. By using the density matrix renormalization group (DMRG) calculation on a cylinder system with a circumference of up to ten lattice sites, we identify a disordered phase between the Néel and stripe magnetic phase with growing $J_2/J_1$ in the presence of strong bond randomness. The vanished spin-freezing parameter indicates the absence of spin-glass order. The large-scale DMRG results unveil the size-scaling behaviors of the spin-freezing parameter, the power-law decay of the average spin correlation, and the exponential decay of the typical spin correlation, which all agree with the corresponding behavior in the one-dimensional random-singlet (RS) state and characterize the RS nature of this disordered phase. The DMRG simulation also provides insights and opportunities for characterizing a class of nonmagnetic states in two-dimensional frustrated magnets with disorder. We also compare with existing experiments and suggest more measurements for understanding the spin-liquid-like behaviors in the double perovskite ${\mathrm{Sr}}_2{\mathrm{CuTe}}_{1-x}{\mathrm{W}}_x{\mathrm{O}}_6$.

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• Frustrated magnetism
• Disordered systems
• Perovskites
• Transition metal oxides
• Density matrix renormalization group