My Ph.D. research focuses on the numerical study of two quantum spin systems, one is the square-lattice Heisenberg antiferromagnet with ring-exchange interaction at the Neel to valence-bond solid state transition, which is proposed to be described by the theory of deconfined criticality; the other is the highly frustrated pyrochlore Heisenberg antiferromagnet. Both systems are known as prototypical candidates for the exotic spin-liquid state with emergent fractionalized excitations and gauge structure. Regarding the long standing controversy of deconfined criticality, our results conclude that the deconfined critical theory capture the essence of the Neel to valence-bond solid state transition at least at intermediate scales of distances, and also suggest that both the deconfined critical point and the Neel to valence-bond solid state transition are weak first-order transitions. In the frustrated pyrochlore Heisenberg antiferromagnet, we found a wide cooperative paramagnetic temperature regime where the system is in an emergent thermal spin-ice state. The conclusion is drawn by a remarkably accurate microscopic correspondence for static structure factor between the quantum Heisenberg model and its classical counterparts. An analysis for the dynamic structure factor obtained by the analytic continuation of numerical data is also performed, showing a result consistent with diffusive spinon dynamics of certain special modes.