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We investigate the ground-state and finite-temperature properties of thebond-random $s=1/2$ Heisenberg model on a honeycomb lattice with frustratednearest- and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and$J_2$, by the exact diagonalization and the Hams--de Raedt methods. Theground-state phase diagram of the model is constructed in the randomness versusthe frustration ($J_2/J_1$) plane, with the aim of clarifying the effects ofrandomness and frustration in stabilizing a variety of distinct phases. We findthat the randomness induces the gapless quantum spin liquid (QSL)-like state,the random-singlet state, in a wide range of parameter space. The observedrobustness of the random-singlet state suggests that the gapless QSL-likebehaviors might be realized in a wide class of frustrated quantum magnetspossessing a certain amount of randomness or inhomogeneity, without fine-tuningthe interaction parameters. Possible implications to recent experiments on thehoneycomb-lattice magnets Ba$_3$CuSb$_2$O$_9$ and 6HB-Ba$_3$NiSb$_2$O$_9$exhibiting the gapless QSL-like behaviors are discussed.

Randomness-induced quantum spin liquid behavior in the s=1/2 random J1-J2 Heisenberg antiferromagnet on the honeycomb lattice