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We study the effects of bond randomness in the spin-$1/2$ $J_1-J_2$triangular Heisenberg model using exact diagonalization and density matrixrenormalization group. With increasing bond randomness, we identify arandomness induced spin-liquid-like phase without any magnetic order, dimerorder, spin glass order, or valence-bond glass order. The finite-size scalingof gaps suggests the gapless nature of both spin triplet and singletexcitations, which is further supported by the broad continuum of dynamicalspin structure factor. By studying the bipartite entanglement spectrum of thesystem on cylinder geometry, we identify the features of the low-lyingentanglement spectrum in the spin-liquid-like phase, which may distinguish thisrandomness induced spin-liquid-like phase and the intrinsic spin liquid phasein the clean $J_1 - J_2$ triangular Heisenberg model. We further discuss thenature of this spin-liquid-like phase and the indication of our results forunderstanding spin-liquid-like materials with triangular-lattice structure.

Randomness induced spin-liquid-like phase in the spin-$1/2$ $J_1 - J_2$ triangular Heisenberg model