Cluster nonequilibrium relaxation in quantum phase transition in the two-dimensional S = 1/2 dimerized antiferromagnetic Heisenberg model

Recently the present authors showed that the stretched-exponential critical relaxation is widely observed in classical spin systems in the nonequilibrium relaxation process of cluster algorithms. In the present article we find that this behavior can be generalized to quantum phase transitions analyzed with the continuous-time loop algorithm, where the cluster update is introduced a prior. As an example, we consider the Néel-dimer quantum phase transition in the two-dimensional S = 1/2 columnar-dimerized antiferromagnetic Heisenberg model on a square lattice, and confirm the stretched-exponential critical relaxation consistent with the three-dimensional classical Heisenberg model in the Swendsen-Wang algorithm.