  The nature of the randomness-induced quantum spin liquid state, the
random-singlet state, is investigated in two dimensions (2D) by means of the
exact-diagonalization and the Hams-de Raedt methods for several frustrated
lattices, e.g., the triangular, the kagome and the J_1-J_2 square lattices.
Properties of the ground state, the low-energy excitations and the
finite-temperature thermodynamic quantities are investigated. The ground state
and the low-lying excited states consist of nearly isolated singlet-dimers,
clusters of resonating singlet-dimers, and orphan spins. Low-energy excitations
are either singlet-to-triplet excitations, diffusion of orphan spins
accompanied by the recombination of nearby singlet-dimers, creation or
destruction of resonating singlet-dimers clusters. The latter two excitations
give enhanced dynamical `liquid-like' features to the 2D random-singlet state.
Comparison is made with the random-singlet state in a 1D chain without
frustration, the similarity and the difference between in 1D and in 2D being
highlighted. Frustration in a wide sense, not only the geometrical one but also
including the one arising from the competition between distinct types of
interactions, play an essential role in stabilizing this frustrated random
singlet state. Recent experimental situations on both organic and inorganic
materials are reviewed and discussed.
