triangular Heisenberg model.*

We study the effects of bond randomness on the antiferromagnetic J₁-J₂ triangular Heisenberg model using exact diagonalization (ED) and density-matrix renormalization group (DMRG). With increasing randomness, we identify a gapless random-singlet (RS) phase without any magnetic order and spin-glass order. Using torus geometries up to 48 sites, we characterize the RS phase using both static and dynamical correlations. The vanishing magnetic order with growing randomness shows the phase boundaries between the magnetic orders (120⁰ Neel and stripe phases) and the RS phase. In addition, We study the effects of randomness in the highly frustrated spin liquid phase of the J₁-J₂ model. We show some signatures of the entanglement spectrum on cylinder geometry that may characterize the phase transition between the two disorder phases. Our numerical results may help to understand the spin liquid behaviors observed in the real materials such as the recently-discovered material YbMgGaO₄ where the mixing of Mg²⁺ and Ca³⁺ ions may introduce randomness to the superexchange.