Static and dynamical spin correlations of the S=1/2 random-bond antiferromagnetic Heisenberg model on the triangular and kagome lattices

Inspired by the recent theoretical suggestion that the random-bond S = 1/2 antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this randomsinglet state might be relevant to the QSL behaviors experimentally observed in triangular organic salts kappa-(ET)(2)Cu-2(CN)(3) and EtMe3Sb[Pd(dmit)(2)](2) and in kagome herbertsmithite ZnCu3(OH)(6)Cl-2, we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors, S(q) and S(q, omega), by means of an exact diagonalization method. In both triangular and kagome models, the computed S(q, omega) in the random-singlet state depends on the wave vector q only weakly, robustly exhibiting gapless behaviors accompanied by the broad distribution extending to higher energy omega. Especially in the strongly random kagome model, S(q, omega) hardly depends on q, and exhibits an almost flat distribution for awide range of omega, together with a omega = 0 peak. These features agree semiquantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite. Furthermore, the computed magnetization curve agrees almost quantitatively with the experimental one recently measured on a single-crystal herbertsmithite. These results suggest that the QSL state observed in herbertsmithite might indeed be the randomness-induced QSL state, i.e., the random-singlet state.