"Temperature scaling" in quantum phase transitions with cluster-update quantum Monte Carlo

Advanced quantum Monte Carlo algorithms such as the loop algorithm [1] are based on the cluster update, and their relaxation has been considered too fast to apply the nonequilibrium relaxation (NER) method based on the power-law critical relaxation [2]. The present authors revealed that the critical cluster NER in classical spin systems is described by the stretched-exponential relaxation [3-6]. They generalized this procedure to the loop algorithm, and analyzed quantum phase transitions with the cluster NER [7]. Recently, the present authors proposed that the off-critical behaviors in classical spin systems can also be analyzed with the NER framework [8], and called this scheme as the "temperature scaling". In the present talk, we generalize this scheme to quantum phase transitions. As an example, we consider the Néel-dimer quantum phase transition in the two-dimensional S=1/2 antiferromagnetic Heisenberg model with columnar dimerization.

[1] H. G. Evertz et al., PRL 70, 875 (1993). [2] Y. Ozeki and N. Ito, J. Phys. A 40, R149 (2007). [3] Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014). [4] YN and Y. Tomita, PRE 92, 062121 (2015). [5] YN and YT, PRE 93, 012101 (2016). [6] YT and YN, PRE 98, 052110 (2018). [7] YN and YT, PRE 101, 032105 (2020). [8] YN and YT, arXiv:2007.14356.