Critical nonequilibrium relaxation in cluster-update quantum Monte Carlo algorithms and its application to quantum phase transitions

Although improved quantum Monte Carlo (QMC) algorithms are based on the cluster-update scheme, previous applications of the nonequilibrium relaxation (NER) scheme to QMC calculations were based on the local-update scheme [1,2] because of “too fast relaxation of the cluster-update scheme for NER analyses”. Recently we found that the critical NER in cluster algorithms is described by the stretched-exponential simulation-time dependence, not the power-law one [3]. In the present study we analyze the Néel-dimer quantum phase transition of the S=1/2 columnar-dimerized antiferromagnetic Heisenberg model on a square lattice with the continuous-time loop algorithm and NER from the isolated dimer configuration. Our estimate of the critical point δ_c≈0.9095 (ratio of the strength of dimerized bonds to normal ones is (1+δ):1) is consistent with a recent QMC estimate δ_c≈0.90947(3) [4], and the relaxation exponent σ is consistent with that of the three-dimensional classical Heisenberg model, σ≈1/2 [5].

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[4] S. Yasuda and S. Todo, Phys. Rev. E 88, 061301(R) (2013).
[5] Y. Nonomura and Y. Tomita, Phys. Rev. E 93, 012101 (2016).